", 2}, {"coding", 2}, {"compensation", 2}, {"crosstalk", 2}, {"data", 2}, {"detection", 2}, {"developed", 2}, {"effects", 2}, {"explored", 2}, {"impact", 2}, {"innovative", 2}, {"investigate", 2}, {"key", 2}, {"light", 2}, {"links", 2}, {"modes", 2}, {"novel", 2}, {"parallel", 2}, {"polarization", 2}, {"promising", 2}, {"propagation", 2}, {"properties", 2}, {"purpose", 2}, {"research", 2}, {"solutions", 2}, {"theoretical", 2}, {"time", 2}}|>, "1500173" -> <|"AwardTitle" -> "EAGER: Rapid, Efficient Implementation of Irregular Applications on SIMD Many-Core Platforms", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2017, 7, 31}], "AwardAmount" -> Quantity[268316, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "05050000", "ProgramOfficer" -> "M. Mimi McClure", "Abstract" -> "General-purpose computation with efficient Single Instruction, Multiple Data (SIMD) oriented many-core devices, such as graphical processing units (GPUs), can deliver high performance in a variety of application domains. Data-parallel applications that perform well on SIMD many-cores typically exhibit regularity in patterns of computation and data movement, acting identically on each of an ensemble of many equal-sized inputs. However, many important applications exhibit irregular behavior making them difficult to implement efficiently on these platforms. Thus, efficient SIMD implementation of applications with irregular behavior is an important ongoing research problem. \n\nThis project's focus is the investigation and validation of novel interface designs, algorithmic techniques, and implementation strategies to address the problem of efficient SIMD implementation uniformly for applications from a variety of domains. The work includes generating alternate module designs to support efficient developer-driven searches over large design spaces to tune performance. Another key area of the research will validate these technologies on bio-sequence analysis applications resulting in innovative, efficient new GPU designs for computational tasks. \n\nMore broadly and with a particular focus on new high-performance application designs for data-intensive computations critical to bioinformatics, the project will enable faster development of more efficient, more maintainable GPU software, even for applications with SIMD-unfriendly irregular behaviors.", "AwardID" -> "1500173", "Institution" -> Entity["NSFInstitution", "WashingtonUniversity"], "Investigators" -> {Entity["NSFInvestigator", "RogerChamberlain"], Entity["NSFInvestigator", "JeremyBuhler"]}, "ProgramElements" -> {{"Code" -> "1714", "Text" -> "SPECIAL PROJECTS - CISE"}, {"Code" -> "7354", "Text" -> "COMPUTER SYSTEMS"}}, "ProgramReferences" -> {{"Code" -> "7916", "Text" -> "EAGER"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Direct For Computer & Info Scie & Enginr", "Division" -> "Division Of Computer and Network Systems", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500173&HistoricalAwards=false"], "KeywordTally" -> {{"applications", 6}, {"efficient", 6}, {"designs", 4}, {"SIMD", 4}, {"implementation", 3}, {"irregular", 3}, {"application", 2}, {"behavior", 2}, {"br/>

", 2}, {"computation", 2}, {"domains", 2}, {"exhibit", 2}, {"focus", 2}, {"GPU", 2}, {"important", 2}, {"new", 2}, {"performance", 2}, {"problem", 2}, {"research", 2}, {"variety", 2}}|>, "1500174" -> <|"AwardTitle" -> "Collaborative Research: Algebra and Algorithms, Structure and Complexity Theory", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[103519, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This project is a collaboration between mathematical researchers at five universities, including young mathematicians at the early stages of their careers, who are joining forces to tackle fundamental problems at the confluence of mathematical logic, algebra, and computer science. The overall goal is to deepen understanding about how to recognize the complexity of certain types of computational problems. The project focuses on a suite of mathematical problems whose solutions will yield new information about the complexity of Constraint Satisfaction Problems. These problems (CSP's) include scheduling problems, resource allocation problems, and problems reducible to solving systems of linear equations. CSP's are theoretically solvable, but some are not solvable efficiently. The research will be aimed at identifying a clear boundary between the tractable and intractable cases, and at providing efficient algorithms for solutions in the tractable cases. Many fundamental problems in mathematics and computer science can be formulated as CSP's, and progress here would have both practical and theoretical significance. A second component of the project investigates classical computational problems in algebra in order to determine whether they are algorithmically solvable. A third component of the project is the further development of the software UACalc, which is a proof assistant developed to handle computations involving algebraic structures.\n\nThe researchers shall work to decide the truth of the CSP Dichotomy Conjecture of Feder and Vardi, which states that every Constraint Satisfaction Problem with a finite template is solvable in polynomial time or is NP complete. They will further develop the algebraic approach to CSP's by refining knowledge about relations compatible with weak idempotent Maltsev conditions and about algebras with finitely related clones. A second goal of the project concerns the computable recognition of properties of finite algebras connected with the varieties they generate, such as whether a finite algebra with a finite residual bound is finitely axiomatizable, or whether a finite algebra can serve as the algebra of character values for a natural duality. One of the more tangible accomplishments of this project will be a broadening and strengthening of the applicability of the UACalc software. The agenda for this part of the project includes parallelizing the important subroutines, building in conjecture-testing and search features, adding further algorithms, and further developing the community of users and contributors.", "AwardID" -> "1500174", "Institution" -> Entity["NSFInstitution", "VanderbiltUniversity"], "Investigators" -> {Entity["NSFInvestigator", "RalphMcKenzie"]}, "ProgramElements" -> {{"Code" -> "1268", "Text" -> "FOUNDATIONS"}, {"Code" -> "1253", "Text" -> "OFFICE OF MULTIDISCIPLINARY AC"}, {"Code" -> "1271", "Text" -> "COMPUTATIONAL MATHEMATICS"}, {"Code" -> "2878", "Text" -> "SPECIAL PROJECTS - CCF"}}, "ProgramReferences" -> {{"Code" -> "7433", "Text" -> "CyberInfra Frmwrk 21st (CIF21)"}, {"Code" -> "7933", "Text" -> "NUM, SYMBOL, & ALGEBRA COMPUT"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9263", "Text" -> "COMPUTATIONAL SCIENCE & ENGING"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500174&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 9}, {"project", 7}, {"algebra", 5}, {"finite", 5}, {"CSP's", 4}, {"solvable", 4}, {"mathematical", 3}, {"algebraic", 2}, {"algebras", 2}, {"algorithms", 2}, {"cases", 2}, {"complexity", 2}, {"component", 2}, {"computational", 2}, {"computer", 2}, {"Constraint", 2}, {"finitely", 2}, {"fundamental", 2}, {"goal", 2}, {"researchers", 2}, {"Satisfaction", 2}, {"science", 2}, {"second", 2}, {"software", 2}, {"solutions", 2}, {"tractable", 2}, {"UACalc", 2}}|>, "1500178" -> <|"AwardTitle" -> "PFI:AIR - TT: High-Reliability Robot Grasping for Per-Item Distribution", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2016, 10, 31}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI:AIR Technology Translation project is aimed at a proof-of-concept demonstration of a robotic grasping system with an error rate of 1 in 10,000 trials or better. In prior NSF-funded work, the researchers developed highly capable, low-cost robot hands which, when paired with a standard industrial robot arm and vision system, can grasp a sufficiently wide range of items to be useful for e-commerce order fulfillment and automated restocking applications. The intended applications, however, require extremely low error rates. This project will (1) develop a system to independently test the reliability of the grasping system on a realistic variety of potential customer inventory, and (2) implement and evaluate new mechanisms for the system to detect and correct errors during grasping.\n\nThe proposed in-depth evaluation of the reliability of grasping systems in real-world tasks is unprecedented. To date, published assessments of grasp system success is limited to a few dozen to a few hundred trials - and typically results in error rates of 1-10%. The proposed methods for evaluation of grasp errors represents an essential capability for validating the performance of robot hands as they move out of laboratories and factories into diverse real-world settings like homes, hospitals, and shop floors. In addition, this project will develop new methods for independently assessing errors in grasping, as well as new methods for enhancing the reliability of grasping. The proposed system will produce very large data sets that will be exploited in future work for data-driven learning of grasp control and on-line error detection and correction. In addition, post docs involved in this project will receive entrepreneurship and technology translation experiences through working to define customer needs and developing application-driven technology.\n\nHigh-reliability automated grasping systems promise to reduce costs and enhance the productivity of the warehousing and logistics businesses that are a rapidly-growing segment of the economy. By automating the selection of inventory from automated storage and retrieval systems, tasks such as order picking, auditing and packing can be accomplished with fewer sources of error, which is crucial in handling high-value products such as pharmaceuticals and electronics. The development of systems and methods for assessing grasping success for diverse object sets will lay the essential groundwork for many imminent real-world applications of grasping in less structured environments.", "AwardID" -> "1500178", "Institution" -> Entity["NSFInstitution", "HarvardUniversity"], "Investigators" -> {Entity["NSFInvestigator", "RobertHowe"], Entity["NSFInvestigator", "ZivthanDubrovsky"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500178&HistoricalAwards=false"], "KeywordTally" -> {{"grasping", 8}, {"system", 7}, {"error", 5}, {"grasp", 4}, {"methods", 4}, {"project", 4}, {"systems", 4}, {"applications", 3}, {"automated", 3}, {"errors", 3}, {"new", 3}, {"proposed", 3}, {"real-world", 3}, {"reliability", 3}, {"robot", 3}, {"1", 2}, {"addition", 2}, {"assessing", 2}, {"customer", 2}, {"develop", 2}, {"diverse", 2}, {"essential", 2}, {"evaluation", 2}, {"hands", 2}, {"independently", 2}, {"inventory", 2}, {"order", 2}, {"rates", 2}, {"sets", 2}, {"success", 2}, {"tasks", 2}, {"trials", 2}, {"work", 2}}|>, "1500180" -> <|"AwardTitle" -> "Asymptotic Methods in Geometric Group Theory", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[288573, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "Modern group theory is a very fast developing area of mathematics that uses methods from algebra, geometry, combinatorics, topology, probability, logic, and computer science. Applications of group theory are ubiquitous throughout science, from physics and chemistry to cyber security. This award supports collaborative research in the area of asymptotic methods in group theory, an area that has been extremely active since seminal papers by Gromov on hyperbolic groups and asymptotic invariants of groups. This project will significantly advance knowledge of the area by solving several open problems. The investigators will advise graduate students, organize research experiences for undergraduate students, and organize conferences on the subject of asymptotic methods in group theory.\n\nThe problems under study in this research project include\n* estimating Dehn functions of metabelian groups;\n* constructing actions of hyperbolic groups resembling Tarski monster groups;\n* constructing simple groups that admit highly transitive actions;\n* describing all possible Tarski numbers of groups; and\n* finding an amenable group with all asymptotic cones tree-graded.\nThe results of the project will advance understanding of asymptotic methods in group theory.", "AwardID" -> "1500180", "Institution" -> Entity["NSFInstitution", "VanderbiltUniversity"], "Investigators" -> {Entity["NSFInvestigator", "MarkSapir"], Entity["NSFInvestigator", "AlexanderOlshanskiy"]}, "ProgramElements" -> {{"Code" -> "1267", "Text" -> "TOPOLOGY"}, {"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500180&HistoricalAwards=false"], "KeywordTally" -> {{"group", 6}, {"asymptotic", 5}, {"groups", 5}, {"area", 4}, {"methods", 4}, {"theory", 4}, {"project", 3}, {"research", 3}, {"advance", 2}, {"constructing", 2}, {"groups;

, "1500184" -> <|"AwardTitle" -> "Non-Archimedean Geometry and its Applications", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 3, 31}], "AwardAmount" -> Quantity[49850, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "The conference \"Non-Archimedean Geometry and its Applications\" will be held at the University of Michigan, Ann Arbor, during the period June 1-5, 2015. It will feature talks by world experts, encourage new collaborations, and serve as an excellent opportunity for junior participants to learn and meet experts in the mathematical field of non-Archimedean geometry. The senior speakers have been chosen on the basis of their research credentials, but also for being superior expositors with a dedication to the development of younger generations of researchers and teachers in mathematics. There will also be several junior speakers, and an opportunity for Ph.D. students and postdocs to present their work in a poster session. A strong effort will be made to have a diverse group of speakers and participants.\n\nThere have been numerous recent advances in non-Archimedean geometry, and these techniques have also seen new and sometimes unexpected applications. In order to make these developments known to a larger mathematical audience, the conference \"Non-Archimedean Geometry and its Applications\" will be held during the period June 1-5, 2015 at the University of Michigan, Ann Arbor. It will bring together leading experts in various fields where non-Archimedean geometry or analysis play an important role, and establish connections between these fields. Among the themes represented at the conference will be Berkovich spaces, tropical geometry, dynamical systems, and p-adic Hodge theory.", "AwardID" -> "1500184", "Institution" -> Entity["NSFInstitution", "UniversityOfMichiganAnnArbor"], "Investigators" -> {Entity["NSFInvestigator", "MattiasJonsson"], Entity["NSFInvestigator", "BhargavBhatt"], Entity["NSFInvestigator", "TylerFoster"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500184&HistoricalAwards=false"], "KeywordTally" -> {{"geometry", 4}, {"conference", 3}, {"experts", 3}, {"non-Archimedean", 3}, {"speakers", 3}, {"1-5", 2}, {"2015", 2}, {"Ann", 2}, {"Applications", 2}, {"Arbor", 2}, {"fields", 2}, {"Geometry", 2}, {"held", 2}, {"June", 2}, {"junior", 2}, {"mathematical", 2}, {"Michigan", 2}, {"new", 2}, {"Non-Archimedean", 2}, {"opportunity", 2}, {"period", 2}, {"University", 2}}|>, "1500186" -> <|"AwardTitle" -> "DDRIG: Expanding Phonological Typology through Kaco' Sound Patterns", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 11, 30}], "AwardAmount" -> Quantity[14500, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Emily Olsen, under the direction of Juliette Blevins of the City University of New York, will conduct a study of the sound system of Kaco', an undescribed minority language spoken in rural Ratanakiri Province, Cambodia. Kaco' is an Austro-Asiatic language of the Mon Khmer family and, like other languages of this family, Kaco' is phonologically complex and unusual. Olsen's study of Kaco' will therefore advance knowledge of what types of phonological systems are possible for human languages. In addition, because sounds and sound processes provide important clues to language relatedness, Olsen's description of Kaco' sound patterns will facilitate hypotheses on the features that are unique to or characteristic of the Austroasiatic language family and will help disambiguate historical relationships between languages and speaker groups of the region.\n\nThe primary research questions involve the description of the sound patterns of the Kaco' language including contrastive vowels and consonants and their phonetic variants, the structure of Kaco' syllables; laryngeal contrasts in Kaco'syllables and their phonetic properties and phonological domains. Olsen's study will focus on documenting complex syllable structure and the role between syllables within a word. She will document phonation (vocal fold vibration) and tonogenesis (e.g., the birth of tone through consonant weakening). \n\nIn order to pursue these research questions, Olsen will collect speech samples from Kaco' speakers from several villages. Her data samples will include recordings of freeform narratives, wordlists, songs, and community folklore. The resulting corpus will be the first cultural and linguistic resource of its kind for use by Kaco' people. This resource will enable development of literacy materials for the community, including a Kaco' orthography, children's books and recordings, and a dictionary.\n\nData from this project will be archived at the Lund University's Repository &\nWorkspace for Austroasiatic Intangible Heritage.", "AwardID" -> "1500186", "Institution" -> Entity["NSFInstitution", "CUNYGraduateSchoolUniversityCenter"], "Investigators" -> {Entity["NSFInvestigator", "JulietteBlevins"], Entity["NSFInvestigator", "EmilyOlsen"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500186&HistoricalAwards=false"], "KeywordTally" -> {{"Kaco", 10}, {"language", 5}, {"sound", 4}, {"family", 3}, {"languages", 3}, {"Olsen's", 3}, {"study", 3}, {"Austroasiatic", 2}, {"community", 2}, {"complex", 2}, {"description", 2}, {"including", 2}, {"Olsen", 2}, {"patterns", 2}, {"phonetic", 2}, {"phonological", 2}, {"questions", 2}, {"recordings", 2}, {"research", 2}, {"resource", 2}, {"samples", 2}, {"structure", 2}, {"syllables", 2}}|>, "1500187" -> <|"AwardTitle" -> "Development and Testing of a Global Quasi-3-D Multi-scale Modeling Framework", "AwardEffectiveDate" -> DateObject[{2016, 2, 1}], "AwardExpirationDate" -> DateObject[{2019, 1, 31}], "AwardAmount" -> Quantity[656746, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "06020106", "ProgramOfficer" -> "Eric T. DeWeaver", "Abstract" -> "Global atmospheric general circulation models (GCMs) used for weather prediction and climate modeling typically divide the atmosphere into a grid, with a single value for atmospheric variables like temperature and pressure in each grid box. As the grid boxes are typically tens of kilometers wide or more it is not possible to represent individual clouds, or even cloud systems, in such models. Instead the net effect of clouds and other small-scale processes on the larger scale atmospheric flow must be approximated through the use of parameterizations, and this representation is a key source of errors in weather forecasts and uncertainty in future climate change projections. Alternative methods of representing clouds and their interactions with large-scale atmospheric conditions are therefore desirable for forecasting the weather and providing decision support to stakeholders concerned with the impacts of climate variability and change.\n\nThis award supports the development and testing of a novel atmospheric model, the global quasi-3D Multiscale Modeling Framework (Q3D MMF). The model is an extension of the Super-Parameterizaton (SP) scheme developed by the Center for Multiscale Modeling of Atmospheric Processes (CMMAP, see AGS-0425247), the Science and Technology Center (STC). The SP MMF consists of a global atmospheric general circulation model (GCM) in which the parameterizations for cloud processes and other subgrid-scale processes in each grid column are replaced by a high-resolution cloud resolving model (CRM). CMMAP has already produced an SP version of the Community Atmosphere Model (CAM, or SP-CAM for the SP version). But SP-CAM uses a two-dimensional (2D) CRM in which the domain is a vertical plane oriented in either the zonal (x-) or meridional (y-) direction and periodic boundary conditions in the x- or y-direction. These restrictions are imposed to reduce computational cost, and to relax them entirely would require a global CRM (GCRM) which is too computationally expensive for most purposes. \n\nAlternatively, the Q3D MMF partially relaxes the conditions by using CRMs with domains that are narrow channels with only a few gridpoints in the cross-channel domain. The channels connect with their counterparts in neighboring cells of the GCM, thus avoiding periodic boundary conditions at either end of the channel. Moreover, each grid cell of the GCM has two such channel-shaped CRMs, oriented in the zonal and meridional direction, to allow for directional anisotropy due to surface topography and other factors.The zonal and meridional CRM channels thus extend around the globe without interruption and intersect each other at adjacent grid cells of the parent GCM. The channel models do not interact at the intersections, as that would result in unphysical behavior associated with a cross-shaped domain. The separate CRM channels communicate only with the GCM, receiving background information from the GCM and supplying the GCM with the outputs expected from standard grid column parameterizations found in conventional GCMs. Work here is an extension of previous work at CMMAP, including the development of a simpler version in which the CRMs are embedded in a regional model over an idealized tropical domain. Work under this award includes several tasks required to develop a global model from this prototype, including inclusion of topography and conversion from a periodic Cartesian domain to a realistic GCM domain.\n\nThe work has broader impacts for the research community because it develops a new atmospheric model which is applicable to a range of research areas related to the impact of clouds on large-scale weather and climate phenomena. To ensure accessibility to the broader research community, the Q3D MMF will be constructed using a version of CAM (the spectral element version) as the GCM component. CAM is freely available, well supported and documented, and widely used, thereby maximizing accessibility. In addition, CAM is the atmospheric component model of the Community Earth System Model, which is used for projections of future climate change that inform decision makers concerned with climate impacts on natural and human systems.", "AwardID" -> "1500187", "Institution" -> Entity["NSFInstitution", "ColoradoStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "DavidRandall"], Entity["NSFInvestigator", "CelalKonor"], Entity["NSFInvestigator", "JOON-HEEJUNG"]}, "ProgramElements" -> {{"Code" -> "5740", "Text" -> "CLIMATE & LARGE-SCALE DYNAMICS"}}, "ProgramReferences" -> {{"Code" -> "OTHR", "Text" -> "OTHER RESEARCH OR EDUCATION"}}, "Directorate" -> "Directorate For Geosciences", "Division" -> "Div Atmospheric & Geospace Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500187&HistoricalAwards=false"], "KeywordTally" -> {{"GCM", 9}, {"atmospheric", 8}, {"model", 8}, {"grid", 7}, {"climate", 6}, {"CRM", 5}, {"domain", 5}, {"version", 5}, {"CAM", 4}, {"channels", 4}, {"clouds", 4}, {"conditions", 4}, {"global", 4}, {"MMF", 4}, {"SP", 4}, {"weather", 4}, {"cloud", 3}, {"CMMAP", 3}, {"CRMs", 3}, {"impacts", 3}, {"meridional", 3}, {"models", 3}, {"parameterizations", 3}, {"periodic", 3}, {"processes", 3}, {"Q3D", 3}, {"research", 3}, {"used", 3}, {"zonal", 3}, {"accessibility", 2}, {"award", 2}, {"boundary", 2}, {"broader", 2}, {"cells", 2}, {"Center", 2}, {"change", 2}, {"channel", 2}, {"circulation", 2}, {"column", 2}, {"community", 2}, {"Community", 2}, {"component", 2}, {"concerned", 2}, {"decision", 2}, {"development", 2}, {"direction", 2}, {"extension", 2}, {"future", 2}, {"GCMs", 2}, {"general", 2}, {"including", 2}, {"large-scale", 2}, {"Model", 2}, {"Modeling", 2}, {"Multiscale", 2}, {"oriented", 2}, {"projections", 2}, {"SP-CAM", 2}, {"systems", 2}, {"topography", 2}, {"typically", 2}, {"using", 2}, {"work", 2}, {"Work", 2}}|>, "1500194" -> <|"AwardTitle" -> "PFI:AIR - TT: Pulsed Shaped Magnetic Fields to Focus Therapy to Deep Tissue Targets", "AwardEffectiveDate" -> DateObject[{2015, 5, 15}], "AwardExpirationDate" -> DateObject[{2016, 10, 31}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation (TT) project aims to enable a safe and effective magnetic focusing of magnetic particle therapies to address inoperable deep tissue tumors. The proposed technique of pulsed magnetic focusing will deliver nanotherapeutics to deep targets in order to direct chemotherapy to where it needs to go in the body. If successful, this technique would enable a technology that could improve treatment for a wide range of diseases. The project will result in a prototype device that will dynamically focus nanorods to deep targets in preclinical studies. In this research, biocompatible nanorods are first aligned in one direction by a fast magnetic pulse, and then before they can turn around a second shaped fast magnetic pulse applies forces on the rods that serve to focus them to a central target. Repeat magnetic pulsing brings all the rods to a central target between the magnets. These features provide the key advantage that therapy can now be focused to a deep target between magnets, for example to treat inoperable deep tissue tumors. Focusing of therapy to deep tissue targets has been a key goal in magnetic drug targeting, and prior efforts in this field have not yet been able to achieve this goal. \n\nThis project addresses the following technology gap(s) as it translates from research discovery toward commercial application. Dynamic magnetic focusing of nanorods to a target between magnets was shown in benchtop experiments. In this NSF AIR TT research, the technology will be tested in tissue samples, scaled up to an in-vivo system, and its safety and utility shall be optimized and verified. In addition, personnel involved in this project will receive innovation, entrepreneurship, and technology translation experiences through developing and helping commercialize this technology.\n\nThe project engages Weinberg Medical Physics who will act as an industry liaison and supply the effort with equipment, expertise, and with connections to strategic partners and future investors in this technology translation effort from research discovery toward commercial reality.", "AwardID" -> "1500194", "Institution" -> Entity["NSFInstitution", "UniversityOfMarylandCollegePark"], "Investigators" -> {Entity["NSFInvestigator", "BenjaminShapiro"], Entity["NSFInvestigator", "IrvingWeinberg"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500194&HistoricalAwards=false"], "KeywordTally" -> {{"magnetic", 8}, {"deep", 6}, {"project", 5}, {"technology", 5}, {"research", 4}, {"target", 4}, {"tissue", 4}, {"focusing", 3}, {"magnets", 3}, {"nanorods", 3}, {"targets", 3}, {"AIR", 2}, {"central", 2}, {"commercial", 2}, {"discovery", 2}, {"effort", 2}, {"enable", 2}, {"fast", 2}, {"focus", 2}, {"goal", 2}, {"inoperable", 2}, {"key", 2}, {"pulse", 2}, {"rods", 2}, {"technique", 2}, {"therapy", 2}, {"translation", 2}, {"TT", 2}, {"tumors", 2}}|>, "1500195" -> <|"AwardTitle" -> "PFI:AIR-TT: Video Collaboratory: A Platform for Active Viewing and Collaboration with Video Data", "AwardEffectiveDate" -> DateObject[{2015, 7, 15}], "AwardExpirationDate" -> DateObject[{2016, 12, 31}], "AwardAmount" -> Quantity[211917, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating an online software technology (The Video Collaboratory) to fill the need for innovative support in small group collaboration and discussion around video documents. The Video Collaboratory is important because increasingly huge amounts of video are being generated for business and personal use. And while there are currently ways to distribute / watch video, it is still not easy to drill into, analyze, and note important details from within the video as a means to an end, particularly when working with others. From corporate training to healthcare, education, and security, people need effective ways to privately converse about, mark up and brainstorm around videos that are linked directly into the video content itself. The project will result in a scaled-up and enhanced Video Collaboratory platform with the following unique features: new ways for precision interaction with video documents, direct connection of group discussions to the video timeline, and private social networking to support meaningful work with videos. These features provide the following advantages: enabling clearer, deeper discussion; reducing error and confusion; and increasing efficiency / saving time when compared to the leading competing technologies in this market space, such as YouTube and Vimeo, that focus on distribution rather than detailed analysis and use of video documents. This project will develop a market-ready technology platform for next-generation collaboration around video data.\n\nThis project addresses the following technology gaps as it translates from research discovery toward commercial application: (1) social presence affordances and group analytics to enable group-guided viewing and synchronous interaction around video documents; (2) rich communication pathways to support multimedia annotations and video-centric filtering of commentary as part of video-anchored discussion; (3) responsive components for interface and video data to scale across platforms (particularly mobile) with smart video streaming that adapts to user network environments; and (4) elastic, scalable, and socially-aware metrics for group/project organization, access/privacy control, and content management for sharing. Significant contributions to the research and knowledge base are novel techniques designed to address these gaps, validated through user study testing. Contributions include techniques for synchronous interaction around video documents; social discussion threading (integrating context from annotated video segmentation, user interaction analytics, and discussion content); weighted adaptive video streaming to prioritize transfer of content by discussion activity; and a flexible, socially-aware model for access management and content sharing. In addition, personnel involved in this project, graduate students and post-docs, will receive technology translation and entrepreneurship experiences through research development and discovery toward commercial reality.", "AwardID" -> "1500195", "Institution" -> Entity["NSFInstitution", "UniversityOfNorthCarolinaAtCharlotte"], "Investigators" -> {Entity["NSFInvestigator", "DavidWilson::ffp5s"], Entity["NSFInvestigator", "CelineLatulipe"], Entity["NSFInvestigator", "SybilHuskey"], Entity["NSFInvestigator", "DevinCollins"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "116E", "Text" -> "RESEARCH EXP FOR UNDERGRADS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500195&HistoricalAwards=false"], "KeywordTally" -> {{"video", 15}, {"discussion", 6}, {"project", 6}, {"content", 5}, {"documents", 5}, {"group", 4}, {"interaction", 4}, {"technology", 4}, {"Collaboratory", 3}, {"following", 3}, {"research", 3}, {"social", 3}, {"support", 3}, {"user", 3}, {"Video", 3}, {"ways", 3}, {"access", 2}, {"analytics", 2}, {"collaboration", 2}, {"commercial", 2}, {"discovery", 2}, {"features", 2}, {"gaps", 2}, {"important", 2}, {"management", 2}, {"need", 2}, {"particularly", 2}, {"platform", 2}, {"sharing", 2}, {"socially-aware", 2}, {"streaming", 2}, {"synchronous", 2}, {"techniques", 2}, {"use", 2}, {"videos", 2}}|>, "1500201" -> <|"AwardTitle" -> "Redox, Electronic, and Rectifying Response of Five- and Six-coordinate Metallosurfactants in Solution, as Films, and on Electrodes", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2018, 4, 30}], "AwardAmount" -> Quantity[449000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03090000", "ProgramOfficer" -> "James Lisy", "Abstract" -> "In this project funded by the Macromolecular, Supramolecular and Nanochemistry Program of the Division of Chemistry, Professor Cláudio N. Verani and his research group at Wayne State University in Detroit are studying metal-based molecules able to act as diodes for electric current rectification. Rectification, or directional current flow from an electrode A to an electrode B (but not from B back to A) is fundamental to the conversion of alternating into direct current, and is absolutely necessary for electronic data computation. This interdisciplinary proposal seeks to enhance our fundamental understanding on the use of metallosurfactants for molecular diodes. Broader impacts include scientific outreach to fourth and fifth graders and effort to promote Latino-student inclusion in STEM research.\n\nVerani and collaborators are studying the redox, electronic, and rectifying behavior of metallosurfactants, both in solution and as Langmuir-Blodgett monolayer films deposited onto gold electrodes. Therefore, this interdisciplinary program focuses on the use of amphiphilic coordination complexes towards current-rectifying assemblies as measured by the asymmetry of current/potential (I/V) curves aiming to understand (i) the predominant rectification mechanisms in metallosurfactants; (ii) the possibility of electron-transfer mediation in metal-based singly occupied molecular orbitals (SOMOs); (iii) the viability of electron transfer mediation by metals between ligand-centered lowest unoccupied & highest occupied molecular orbitals (LUMOS & HOMOs); (iv) the role of metallosurfactant orientation in the mechanism of rectification; (v) the influence of the metallosurfactant geometry in observed symmetric conduction, unimolecular or asymmetric rectification, or insulation. This research is multi-faceted, incluidng efforts to make strides in synthetic methodologies, and in electrochemical, spectroscopic, computational, isothermal compression, and microscopy methods.", "AwardID" -> "1500201", "Institution" -> Entity["NSFInstitution", "WayneStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "ClaudioVerani"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Chemistry", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500201&HistoricalAwards=false"], "KeywordTally" -> {{"current", 4}, {"rectification", 4}, {"metallosurfactants", 3}, {"molecular", 3}, {"B", 2}, {"diodes", 2}, {"electrode", 2}, {"electronic", 2}, {"fundamental", 2}, {"interdisciplinary", 2}, {"mediation", 2}, {"metal-based", 2}, {"metallosurfactant", 2}, {"occupied", 2}, {"orbitals", 2}, {"research", 2}, {"studying", 2}, {"use", 2}}|>, "1500204" -> <|"AwardTitle" -> "PFI:AIR - TT: Ultra-fast electro-optical switching of nematic liquid crystals", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2016, 12, 31}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating two recently discovered effects to fill the need for fast switching of liquid crystal (LC) electro-optic devices. Fast switching of light propagation is of prime importance in applications such as optical communications and computing as it allows one to process larger amounts of information within a shorter period of time. The two discovered effects are the Nanosecond Electrically Modified Order Parameter (NEMOP), in which the electric field is used to alter the refractive indices of the LC rather than to reorient the optic axis as in standard approach used so far, and the polymer-induced modification of the order parameter that allows one to enhance the amplitude of the switched optical birefringence. The NEMOP-based technology has the following unique features: the switching time of optical properties is on the order of nanoseconds and tens of nanoseconds; moreover, the switching-on and switching-off responses are equally fast. These features provide the advantages when compared to the leading competing LC switches based on reorientation of the optic axis, as the nanosecond switching is million times faster than the current industry standard of a few milliseconds.\n\nThe NEMOP-based technology brings a new paradigm in the development of LC devices by utilizing microscopic effects of molecular alignment instead of macroscopic reorientation. This project addresses the following technology gaps: relatively high operating voltages (hundreds of volts) and moderate (10-3-10-2) modulation of the effective refractive index, as it translates from research discovery toward commercial application. The researchers will overcome the gaps by a synergy of approaches: (a) polymer modification of the LC materials to increase the amplitude of switching; (b) exploration of LC structure-property relationships in order to enhance the optical response and lower the driving field; (c) design of electro-optic cells that increases the pathway of light propagation. The main commercial target is communication industry where cheap and light-weight LC optical and infrared modulators with nanosecond response times would be of great value. In addition, personnel involved in this project includes several graduate students, who will receive innovation and entrepreneurship experiences through the cutting-edge research, targeted development of the technology to the commercialization level, and through participation in the NSF I-Corps program.", "AwardID" -> "1500204", "Institution" -> Entity["NSFInstitution", "KentStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "OlegLavrentovich"], Entity["NSFInvestigator", "SergijShiyanovskii"], Entity["NSFInvestigator", "SugunaRachakonda"], Entity["NSFInvestigator", "WilliamSouthards"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500204&HistoricalAwards=false"], "KeywordTally" -> {{"LC", 7}, {"optical", 5}, {"switching", 5}, {"technology", 4}, {"effects", 3}, {"order", 3}, {"project", 3}, {"allows", 2}, {"amplitude", 2}, {"axis", 2}, {"commercial", 2}, {"development", 2}, {"devices", 2}, {"discovered", 2}, {"electro-optic", 2}, {"enhance", 2}, {"fast", 2}, {"features", 2}, {"field", 2}, {"following", 2}, {"gaps", 2}, {"industry", 2}, {"light", 2}, {"modification", 2}, {"nanosecond", 2}, {"nanoseconds", 2}, {"NEMOP-based", 2}, {"optic", 2}, {"propagation", 2}, {"refractive", 2}, {"reorientation", 2}, {"research", 2}, {"response", 2}, {"standard", 2}, {"switching-", 2}, {"time", 2}, {"times", 2}, {"used", 2}}|>, "1500205" -> <|"AwardTitle" -> "PFI:AIR - TT: Design Optimization on the Cloud", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[197508, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating the Pareto method of design optimization, developed by the PI's group, into a cloud-based service that can be accessed by designers without the expense of special hardware or software. The Pareto design method is important, and particularly relevant in a cloud-based service, because it offers unprecedented speed at low computational cost. This increases accessibility of design optimization tools across a number of industries, allowing smaller firms to engage in design optimization. The project will result in CloudTopopt, a design optimization cloud service with the following unique features: (a) it can be accessed by anyone, at any time, from any browser such as Firefox, Chrome, Safari or Internet Explorer, (b) it will offer the latest technology and design optimization features, and (c) it will help designers reduce the cost of their end-products through real-time optimization. These features provide the following advantages: (1) it will level the playing field in product design by providing equal access to high quality design software, to large corporations, small firms and individual consultants, (2) it will result in significant cost savings since users will not have to purchase expensive design software and associated hardware, and (3) software and technology updates will be carried out with little or no interference in the product design process. This is in contrast to leading design software modules that require expensive software/hardware installation and maintenance that only large corporations can afford.\n\nThis project addresses the following technology gaps as it translates from research discovery toward commercial application: (1) sustaining the speed of the Pareto method in a cloud service by minimizing the overhead of network communication and browser computation, (2) ensuring cloud security by relying on secure https URLs (Uniform Resource Locator), and data encryption based on industry standard 256 bit AES (Advanced Encryption Standard), and (3) providing a robust user experience by relying on modern WebGL (Web Graphics Library) technology. The personnel involved in this project include an engineering graduate student and a management graduate student. The two students will receive technology translation and entrepreneurship experiences by addressing the technological gaps, and studying the market potential for CloudTopopt, respectively.\n\nThe project engages Design Concepts, LLC (Madison) to guide the technological development and commercialization in this technology translation effort from research discovery toward commercial reality.", "AwardID" -> "1500205", "Institution" -> Entity["NSFInstitution", "UniversityOfWisconsin-Madison"], "Investigators" -> {Entity["NSFInvestigator", "KrishnanSuresh"], Entity["NSFInvestigator", "JonathanEckhardt"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500205&HistoricalAwards=false"], "KeywordTally" -> {{"design", 11}, {"optimization", 6}, {"software", 6}, {"technology", 6}, {"project", 5}, {"service", 4}, {"cloud", 3}, {"cost", 3}, {"features", 3}, {"following", 3}, {"hardware", 3}, {"method", 3}, {"Pareto", 3}, {"1", 2}, {"2", 2}, {"3", 2}, {"accessed", 2}, {"browser", 2}, {"cloud-based", 2}, {"CloudTopopt", 2}, {"commercial", 2}, {"corporations", 2}, {"designers", 2}, {"discovery", 2}, {"expensive", 2}, {"firms", 2}, {"gaps", 2}, {"graduate", 2}, {"large", 2}, {"product", 2}, {"providing", 2}, {"relying", 2}, {"research", 2}, {"result", 2}, {"speed", 2}, {"student", 2}, {"technological", 2}, {"translation", 2}}|>, "1500208" -> <|"AwardTitle" -> "PFI:AIR - TT: Prototyping a Smart Battery Gauge Technology for Stationary Energy Storage of Renewable Energy Resources", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2017, 9, 30}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on developing a novel Smart Battery Gauge technology to fill the increasing need for accurate battery state of charge (SOC) and remaining useful life (RUL) estimations for stationary energy storage systems of renewable energy resources. There is a growing demand for stationary energy storage driven by the increasing interest in the large-scale integration of renewable energy into the power grid. However, major barriers preventing widespread stationary energy storage deployment are safety and reliability concerns. By providing more accurate state of charge and remaining useful life estimates, the Smart Battery Gauge technology will improve safety and reliability and enable the widespread use of stationary battery systems within the emerging renewable energy market. This will drive wider deployment of renewable energy systems, which will help meet the renewable portfolio standards targets imposed by many states. \n\nThis project will result in a software prototype of the Smart Battery Gauge technology to demonstrate its real-time adaptive battery SOC and RUL estimations with market-leading accuracy and reliability, and its flexible customization for multiple different battery chemistries. As compared to the existing battery monitoring methods in the market, the estimation data generated by this technology will provide systems management and operations with the advantages of improved energy storage system efficiency, reliability, cost-effectiveness, longer lifespan, and reduced capital and operation/maintenance costs.\n\nThis project addresses the following shortcomings of existing battery monitoring solutions: 1) State-of-the-art battery SOC estimation methods lack accuracy because of non-updating parameters, 2) State-of-the-art battery RUL estimation methods either do not exist or lack accuracy because of unreliable energy consumption and battery degradation predictions, and 3) State-of-the-art battery SOC and RUL estimation methods is tailored to specific battery chemistry. This project addresses these limitations through research efforts in the following areas: 1) Extraction of the relevant data and models that are needed for accurate RUL estimation; 2) Design of the adaptive predictive RUL estimation algorithm that can adjust the battery parameters with real-time measurement feedback; 3) The development of flexible battery SOC and RUL estimates using a configurable battery model; and 4) Benchmark the Smart Battery Gauge prototype with existing approaches and competing technologies. This project plans to establish collaborations with domestic and international renewable energy companies, as well as provide outreach to other institutions performing renewables and battery related research. In addition, the graduate students involved in this project will receive technology translation and entrepreneurship experiences through the prototype development and commercialization activities.", "AwardID" -> "1500208", "Institution" -> Entity["NSFInstitution", "NorthCarolinaStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "DineshDivakaran"], Entity["NSFInvestigator", "Mo-YuenChow"], Entity["NSFInvestigator", "JasonLamb"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500208&HistoricalAwards=false"], "KeywordTally" -> {{"battery", 15}, {"energy", 10}, {"RUL", 7}, {"estimation", 6}, {"project", 6}, {"renewable", 6}, {"SOC", 5}, {"technology", 5}, {"Battery", 4}, {"Gauge", 4}, {"methods", 4}, {"reliability", 4}, {"Smart", 4}, {"stationary", 4}, {"storage", 4}, {"systems", 4}, {"accuracy", 3}, {"accurate", 3}, {"existing", 3}, {"prototype", 3}, {"State---art", 3}, {"1", 2}, {"2", 2}, {"3", 2}, {"adaptive", 2}, {"addresses", 2}, {"charge", 2}, {"data", 2}, {"deployment", 2}, {"development", 2}, {"estimates", 2}, {"estimations", 2}, {"flexible", 2}, {"following", 2}, {"increasing", 2}, {"lack", 2}, {"life", 2}, {"market", 2}, {"monitoring", 2}, {"parameters", 2}, {"provide", 2}, {"real-time", 2}, {"remaining", 2}, {"research", 2}, {"safety", 2}, {"state", 2}, {"useful", 2}, {"widespread", 2}}|>, "1500216" -> <|"AwardTitle" -> "Collaborative Research: Algebra and Algorithms, Structure and Complexity Theory", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[67889, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This project is a collaboration between mathematical researchers at five universities, including young mathematicians at the early stages of their careers, who are joining forces to tackle fundamental problems at the confluence of mathematical logic, algebra, and computer science. The overall goal is to deepen understanding about how to recognize the complexity of certain types of computational problems. The project focuses on a suite of mathematical problems whose solutions will yield new information about the complexity of Constraint Satisfaction Problems. These problems (CSP's) include scheduling problems, resource allocation problems, and problems reducible to solving systems of linear equations. CSP's are theoretically solvable, but some are not solvable efficiently. The research will be aimed at identifying a clear boundary between the tractable and intractable cases, and at providing efficient algorithms for solutions in the tractable cases. Many fundamental problems in mathematics and computer science can be formulated as CSP's, and progress here would have both practical and theoretical significance. A second component of the project investigates classical computational problems in algebra in order to determine whether they are algorithmically solvable. A third component of the project is the further development of the software UACalc, which is a proof assistant developed to handle computations involving algebraic structures.\n\nThe researchers shall work to decide the truth of the CSP Dichotomy Conjecture of Feder and Vardi, which states that every Constraint Satisfaction Problem with a finite template is solvable in polynomial time or is NP complete. They will further develop the algebraic approach to CSP's by refining knowledge about relations compatible with weak idempotent Maltsev conditions and about algebras with finitely related clones. A second goal of the project concerns the computable recognition of properties of finite algebras connected with the varieties they generate, such as whether a finite algebra with a finite residual bound is finitely axiomatizable, or whether a finite algebra can serve as the algebra of character values for a natural duality. One of the more tangible accomplishments of this project will be a broadening and strengthening of the applicability of the UACalc software. The agenda for this part of the project includes parallelizing the important subroutines, building in conjecture-testing and search features, adding further algorithms, and further developing the community of users and contributors.", "AwardID" -> "1500216", "Institution" -> Entity["NSFInstitution", "UniversityOfSouthCarolinaAtColumbia"], "Investigators" -> {Entity["NSFInvestigator", "GeorgeMcNulty"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500216&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 9}, {"project", 7}, {"algebra", 5}, {"finite", 5}, {"CSP's", 4}, {"solvable", 4}, {"mathematical", 3}, {"algebraic", 2}, {"algebras", 2}, {"algorithms", 2}, {"cases", 2}, {"complexity", 2}, {"component", 2}, {"computational", 2}, {"computer", 2}, {"Constraint", 2}, {"finitely", 2}, {"fundamental", 2}, {"goal", 2}, {"researchers", 2}, {"Satisfaction", 2}, {"science", 2}, {"second", 2}, {"software", 2}, {"solutions", 2}, {"tractable", 2}, {"UACalc", 2}}|>, "1500217" -> <|"AwardTitle" -> "Radical Chemistry on Cloud and Aerosol Surfaces", "AwardEffectiveDate" -> DateObject[{2014, 9, 1}], "AwardExpirationDate" -> DateObject[{2016, 8, 31}], "AwardAmount" -> Quantity[269915, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03090000", "ProgramOfficer" -> "Tyrone D. Mitchell", "Abstract" -> "The Environmental Chemical Sciences Program in the Chemistry Division at the National Science Foundation supports the research of Professors Joseph S. Francisco and Sabre Kais both from Purdue University who will examine how free radicals contribute to numerous significant chemical processes in the atmosphere. Aerosols and cloud droplets play an important role in both the removal and the conversion of gases in the atmosphere. The interactions between gas-phase species on liquid surfaces are central to understanding chemistry at these interfaces. The overall goal of this award is to provide a theoretical framework, based on first principles including classical and ab initio molecular dynamics (MD) simulations, density functional theory combined with finite element methods for Car-Parrinello simulations, and finite size scaling for universal behavior of free energies and other thermodynamic quantities to understand how atmospheric free radicals accommodate and react at the gas-liquid interface.\n\nResults of this project will help improve our understanding of the contribution to radical accommodation and uptake leading to more effective pollution control strategies as well as the improvement in air quality for pollutants whose chemistry is highly coupled to atmospheric free radicals. This multidisciplinary project will bring both undergraduate and graduate students from the departments of Chemistry and Earth and Atmospheric Sciences into the research environment. Moreover, this project will promote and support broader efforts to recruit minority and underrepresented graduate students to the chemical physics program at Purdue University.", "AwardID" -> "1500217", "Institution" -> Entity["NSFInstitution", "UniversityOfNebraska-Lincoln"], "Investigators" -> {Entity["NSFInvestigator", "JosephFrancisco"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Chemistry", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500217&HistoricalAwards=false"], "KeywordTally" -> {{"free", 4}, {"project", 3}, {"radicals", 3}, {"atmosphere", 2}, {"atmospheric", 2}, {"chemical", 2}, {"chemistry", 2}, {"Chemistry", 2}, {"finite", 2}, {"graduate", 2}, {"Purdue", 2}, {"research", 2}, {"Sciences", 2}, {"simulations", 2}, {"students", 2}, {"understanding", 2}, {"University", 2}}|>, "1500218" -> <|"AwardTitle" -> "Collaborative Research: Algebra and Algorithms, Structure and Complexity Theory", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[106881, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This project is a collaboration between mathematical researchers at five universities, including young mathematicians at the early stages of their careers, who are joining forces to tackle fundamental problems at the confluence of mathematical logic, algebra, and computer science. The overall goal is to deepen understanding about how to recognize the complexity of certain types of computational problems. The project focuses on a suite of mathematical problems whose solutions will yield new information about the complexity of Constraint Satisfaction Problems. These problems (CSP's) include scheduling problems, resource allocation problems, and problems reducible to solving systems of linear equations. CSP's are theoretically solvable, but some are not solvable efficiently. The research will be aimed at identifying a clear boundary between the tractable and intractable cases, and at providing efficient algorithms for solutions in the tractable cases. Many fundamental problems in mathematics and computer science can be formulated as CSP's, and progress here would have both practical and theoretical significance. A second component of the project investigates classical computational problems in algebra in order to determine whether they are algorithmically solvable. A third component of the project is the further development of the software UACalc, which is a proof assistant developed to handle computations involving algebraic structures.\n\nThe researchers shall work to decide the truth of the CSP Dichotomy Conjecture of Feder and Vardi, which states that every Constraint Satisfaction Problem with a finite template is solvable in polynomial time or is NP complete. They will further develop the algebraic approach to CSP's by refining knowledge about relations compatible with weak idempotent Maltsev conditions and about algebras with finitely related clones. A second goal of the project concerns the computable recognition of properties of finite algebras connected with the varieties they generate, such as whether a finite algebra with a finite residual bound is finitely axiomatizable, or whether a finite algebra can serve as the algebra of character values for a natural duality. One of the more tangible accomplishments of this project will be a broadening and strengthening of the applicability of the UACalc software. The agenda for this part of the project includes parallelizing the important subroutines, building in conjecture-testing and search features, adding further algorithms, and further developing the community of users and contributors.", "AwardID" -> "1500218", "Institution" -> Entity["NSFInstitution", "IowaStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "CliffordBergman"]}, "ProgramElements" -> {{"Code" -> "1253", "Text" -> "OFFICE OF MULTIDISCIPLINARY AC"}, {"Code" -> "1268", "Text" -> "FOUNDATIONS"}, {"Code" -> "1271", "Text" -> "COMPUTATIONAL MATHEMATICS"}, {"Code" -> "2878", "Text" -> "SPECIAL PROJECTS - CCF"}}, "ProgramReferences" -> {{"Code" -> "7433", "Text" -> "CyberInfra Frmwrk 21st (CIF21)"}, {"Code" -> "7933", "Text" -> "NUM, SYMBOL, & ALGEBRA COMPUT"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}, {"Code" -> "9263", "Text" -> "COMPUTATIONAL SCIENCE & ENGING"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500218&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 9}, {"project", 7}, {"algebra", 5}, {"finite", 5}, {"CSP's", 4}, {"solvable", 4}, {"mathematical", 3}, {"algebraic", 2}, {"algebras", 2}, {"algorithms", 2}, {"cases", 2}, {"complexity", 2}, {"component", 2}, {"computational", 2}, {"computer", 2}, {"Constraint", 2}, {"finitely", 2}, {"fundamental", 2}, {"goal", 2}, {"researchers", 2}, {"Satisfaction", 2}, {"science", 2}, {"second", 2}, {"software", 2}, {"solutions", 2}, {"tractable", 2}, {"UACalc", 2}}|>, "1500219" -> <|"AwardTitle" -> "Extremal graph theory, graph limits, and algebraic invariants", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[151604, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "In this project, the PI aims to study very large networks using algebraic and analytic tools. Large networks like the Internet, molecular lattices and social networks (such as Facebook) naturally arise in many different areas of real life. The PI aims to look at these from a new perspective: we consider them as approximations of an infinite object. For molecular lattices this is a very natural approach, but via a recently developed theory of sparse graph convergence we can tackle a much broader class of problems, creating new links between mathematics, statistical physics and computer science.\n\nThe PI will investigate two essentially different, but still related topics. The first one is the study of extremal values of algebraic invariants of graphs with a special emphasis on those problems where the conjectured extremal graphs are not finite. Despite the lack of finite extremal solutions, using the recently emerging language of Benjamini--Schramm convergence, one can find and analyze the extremal solutions. This then leads to new asymptotic results on finite graphs. The second topic is the study of certain special infinite graphs and lattices via graph limit theory and analytic and algebraic combinatorics. The general theme is to consider a graph invariant of algebraic nature and analyze its limiting behaviour using analytic tools. Often the invariants come from graph polynomials like the matching, chromatic and independence polynomials and have various ties to statistical mechanics.", "AwardID" -> "1500219", "Institution" -> Entity["NSFInstitution", "MassachusettsInstituteOfTechnology"], "Investigators" -> {Entity["NSFInvestigator", "PeterCsikvari"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500219&HistoricalAwards=false"], "KeywordTally" -> {{"algebraic", 4}, {"extremal", 4}, {"graph", 4}, {"graphs", 4}, {"analytic", 3}, {"finite", 3}, {"lattices", 3}, {"networks", 3}, {"new", 3}, {"PI", 3}, {"study", 3}, {"using", 3}, {"aims", 2}, {"analyze", 2}, {"consider", 2}, {"convergence", 2}, {"different", 2}, {"infinite", 2}, {"invariants", 2}, {"like", 2}, {"molecular", 2}, {"polynomials", 2}, {"problems", 2}, {"recently", 2}, {"solutions", 2}, {"special", 2}, {"statistical", 2}, {"theory", 2}, {"tools", 2}, {"via", 2}}|>, "1500220" -> <|"AwardTitle" -> "COLLBORATIVE RESEARCH: CREATING AN AUDIO-VISUAL CORPUS OF SCOTTISH GAIDHLIG TO PRESERVE AND INVESTIGATE LINGUISTIC DIVERSITY", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 11, 30}], "AwardAmount" -> Quantity[152529, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Joan Maling", "Abstract" -> "Scottish Gaelic, a Celtic language closely related to Irish and Welsh and more distantly to English, was once spoken across Scotland by most of the country's population. Today, however, Gaelic remains a community language only in the most remote regions of western Scotland. Gaelic speakers comprise about 1% of the Scottish population; the 2011 census found only 57,375 native speakers, compared to 250,000 a century earlier. This sharp decline makes the language's continued survival uncertain. \n\nScottish Gaelic is of immense interest because it possesses many rare linguistic features, including initial consonant mutation where a word-initial consonant can be changed depending on what the function of that word is in a clause. Scottish Gaelic also exhibits pre-aspirated consonants, and verb-initial sentence structure. In addition, Scottish Gaelic offers remarkable examples of how knowledge systems particular to its local geography and climate (land management, fishing techniques) are imbedded in the language. Should Gaelic become extinct, the global community -- not just Scotland -- will lose an irreplaceable cultural and scientific resource. \n\nThrough this two-year project for $189,457, Professors Ian Clayton from the University of Nevada, Reno along with Andrew Carnie and Mike Hammond from the University of Arizona will create a corpus of linguistic interviews with 30 native Gaelic speakers, with the help of native speaker Muriel Fisher (recipient of the Linguistic Society of America's 2015 Excellence in Community Linguistics Award). Speakers will represent a range of ages, geographic origins, and professional backgrounds. The collection will contain more than twenty hours of high-quality audio-visual material, transcribed and translated, with both cultural and scientific value. The collection will offer an invaluable tool to help linguists expand their scientific study of the language's rare features. In addition, the interviews will focus on traditional occupations, folklore, and oral history, the kinds of knowledge and terminology most at risk as Gaelic declines. \n\nWhen complete, the corpus will be publically available through the Max Planck Institute's Language Archive, and the University of Arizona's Open Repository.", "AwardID" -> "1500220", "Institution" -> Entity["NSFInstitution", "UniversityOfArizona"], "Investigators" -> {Entity["NSFInvestigator", "MichaelHammond"], Entity["NSFInvestigator", "AndrewCarnie"], Entity["NSFInvestigator", "MurielFisher"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500220&HistoricalAwards=false"], "KeywordTally" -> {{"Gaelic", 9}, {"Scottish", 4}, {"language", 3}, {"native", 3}, {"scientific", 3}, {"Scotland", 3}, {"speakers", 3}, {"University", 3}, {"addition", 2}, {"br/>

", 2}, {"collection", 2}, {"community", 2}, {"consonant", 2}, {"corpus", 2}, {"cultural", 2}, {"features", 2}, {"help", 2}, {"interviews", 2}, {"knowledge", 2}, {"language's", 2}, {"linguistic", 2}, {"population", 2}, {"rare", 2}}|>, "1500222" -> <|"AwardTitle" -> "PFI:AIR - TT: BaTiO3 Photonic Crystal Electro-optic Devices for 50 GHz Applications", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2017, 2, 28}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI Accelerating Innovation Technology Project focuses on the development of a prototype Photonic crystal (PhC) electro-optic modulator for ultra-high bandwidth optical systems. This is important because in the future, communication and cyber systems will require optical subsystems with ultra-high transmission rates due to the connectivity requirements of data centers, residential systems, mobile smartphones, and smart network communications. The optical modulator is a key piece of optical systems and at present is the component that limits the data transmission rates. This project focuses on developing a working, packaged prototype optical modulator based on barium titanate (BaTiO3) ferroelectric oxide thin films with a bandwidth of 50 GHz, which is 25% higher than the current state of the art technology based on Lithium niobate (LiNbO3). \n\nLithium niobate (LiNbO3) has been established as the electro-optic material of choice for optical modulators due to its relatively high electro-optic (EO) coefficient. However, it has a high dielectric constant at microwave frequencies, which limits the bandwidth of conventional modulators to 40 gigahertz (GHz) or less. Approaches based on silicon, indium phosphide and polymeric materials have been widely investigated to solve this major challenge and although progress has been made, a number of significant challenges in speed and power required remain. This project takes an alternative approach by using BaTiO3 ferroelectric oxide thin films with experimentally demonstrated electro-optic (EO) coefficients more than an order of magnitude higher than that of LiNbO3. In this project, packaged EO modulators with photonic crystal waveguide structure will be developed. Devices will be fabricated using vapor phase epitaxial deposition, and both conventional photolithography and focused ion beam milling. The BaTiO3 thin film platform has numerous competitive advantages over other platforms for optical modulator applications such as (1) Large EO coefficient, ten times higher compared to those of LiNbO3 devices dominating optical modulator markets; (2) Low driving voltage thus low power consumption; (3) Ultrahigh bandwidth higher than 50 GHz demonstrated with potential reaching sub-THz regime; (4) potential for integration with Si electronics leading to ultrahigh compact electro-optical components at low cost. By using a BaTiO3 thin film platform with non-linear photonic crystals, significant improvements in bandwidth, operating voltage, and size are expected compared to conventional devices. A working packaged, prototype 50 GHz bandwidth modulator, 1mm long, will be demonstrated. The project will involve training of graduate students and postdoctoral scholars in photonic crystal design as well as offering experiences with technology transfer through the development and demonstration of the prototype.", "AwardID" -> "1500222", "Institution" -> Entity["NSFInstitution", "NorthwesternUniversity"], "Investigators" -> {Entity["NSFInvestigator", "BruceWessels"], Entity["NSFInvestigator", "ZhifuLiu"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500222&HistoricalAwards=false"], "KeywordTally" -> {{"optical", 8}, {"bandwidth", 6}, {"modulator", 6}, {"BaTiO3", 4}, {"electro-optic", 4}, {"EO", 4}, {"GHz", 4}, {"higher", 4}, {"LiNbO3", 4}, {"project", 4}, {"prototype", 4}, {"systems", 4}, {"thin", 4}, {"50", 3}, {"based", 3}, {"conventional", 3}, {"crystal", 3}, {"demonstrated", 3}, {"modulators", 3}, {"packaged", 3}, {"photonic", 3}, {"using", 3}, {"coefficient", 2}, {"compared", 2}, {"data", 2}, {"development", 2}, {"devices", 2}, {"due", 2}, {"ferroelectric", 2}, {"film", 2}, {"films", 2}, {"focuses", 2}, {"high", 2}, {"limits", 2}, {"low", 2}, {"niobate", 2}, {"oxide", 2}, {"platform", 2}, {"potential", 2}, {"power", 2}, {"rates", 2}, {"significant", 2}, {"technology", 2}, {"transmission", 2}, {"ultra-high", 2}, {"voltage", 2}, {"working", 2}}|>, "1500224" -> <|"AwardTitle" -> "Dust Transport in Convectively Stratified Atmospheric Boundary Layer", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2018, 3, 31}], "AwardAmount" -> Quantity[148723, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "06020105", "ProgramOfficer" -> "Nicholas F. Anderson", "Abstract" -> "Severe wind erosion and dust storms are a concern in the south central and southwestern parts of the United States. Prolonged drought conditions enhance the potential for Aeolian transport, where wind has the ability to transport and deposit materials such as sand and dirt. Advances in numerical modeling of the near-surface boundary layer of the atmosphere have made it possible to better connect the atmospheric and surface processes involved in Aeolian transport, in order to better understand how and when dust events will occur. The results of this study will be a step towards providing better information on which to make decisions regarding water resources and land use. The study will also include a variety of educational and outreach activities to connect the research to students and the public.\n\nThis award will provide funding for a study on the characteristics of neutrally and convectively stratified atmospheric boundary layer flows with a particular focus on flow over sparsely vegetated, semi-arid landscapes on the west Texas panhandle region of the Southern High Plains. The location of interest is known for severe wind erosion and dust storms, and the minimal topographic relief makes the region ideal for fundamental research studies with large-eddy simulation (LES) models. Modeling aspects of the proposal will be grounded by the use of field data courtesy of a collaboration with the US Department of Agriculture. Specific tasks will include: determining the potential to anchor low- and high-momentum regions in the flow using isolated obstacles, determining the role of solar heating in modifying the turbulence structure, and incorporating transport of suspended dust and inertial sediment into the LES code.", "AwardID" -> "1500224", "Institution" -> Entity["NSFInstitution", "UniversityOfTexasAtDallas"], "Investigators" -> {Entity["NSFInvestigator", "WilliamAnderson"]}, "ProgramElements" -> {{"Code" -> "1525", "Text" -> "PHYSICAL & DYNAMIC METEOROLOGY"}}, "ProgramReferences" -> {{"Code" -> "0000", "Text" -> "UNASSIGNED"}, {"Code" -> "9178", "Text" -> "UNDERGRADUATE EDUCATION"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}, {"Code" -> "OTHR", "Text" -> "OTHER RESEARCH OR EDUCATION"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Directorate For Geosciences", "Division" -> "Div Atmospheric & Geospace Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500224&HistoricalAwards=false"], "KeywordTally" -> {{"dust", 4}, {"transport", 4}, {"better", 3}, {"study", 3}, {"wind", 3}, {"Aeolian", 2}, {"atmospheric", 2}, {"boundary", 2}, {"connect", 2}, {"determining", 2}, {"erosion", 2}, {"flow", 2}, {"include", 2}, {"layer", 2}, {"LES", 2}, {"potential", 2}, {"region", 2}, {"research", 2}, {"storms", 2}, {"use", 2}}|>, "1500234" -> <|"AwardTitle" -> "PFI:AIR - TT: Design of functionally-tested, genomics-informed personalized cancer therapy drug treatment plans", "AwardEffectiveDate" -> DateObject[{2015, 8, 15}], "AwardExpirationDate" -> DateObject[{2017, 1, 31}], "AwardAmount" -> Quantity[194432, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating mathematical modeling and design of combination therapy based on Probabilistic Target Inhibition Maps to fulfill the unmet clinical need of developing functional and genomic-informed personalized cancer therapy. The goal is to improve treatment outcomes by directly addressing drug synergy and disease recurrence. Successful implementation of the Probabilistic Target Inhibition Map innovation is expected to have a significant impact on society by providing an alternative approach to therapy design for cancer patients who have failed, or want alternatives to, first and second line therapies. Even with advances in chemotherapy and radiation, there are over 450,000 deaths attributed to solid tumor cancers in the U.S. alone; resulting in a significant need for alternative approaches involving personalized drug combinations for cancer patients failing standard of care treatments. The project will result in proof of concept validation for application of Probabilistic Target Inhibition Maps to synergistic drug combination design. The Probabilistic Target Inhibition Map framework has the unique features of (i) integrating functional and genomic data in model generation, (ii) increased prediction accuracy over existing techniques and (iii) optimized selection of drug combinations from FDA-approved targeted drugs. This approach will provide rapid, evidenced-based, reduced toxicity personalized therapies, leading to greater treatment efficacy and lower chances of recurrence. The resulting technology will be unlike existing precision cancer therapy approaches available in the market, and will be very competitive with comparable approaches.\n\nThis project addresses the following technology gaps as it translates from research discovery towards commercial application: (a) characterizing combination drug toxicities by incorporating existing side effects data of individual drugs to predict expected system-level toxicity, and integrate additional compound-level and patient-level data to identify potentially unexpected toxicity issues, (b) design of optimization algorithms for selection of drug combinations incorporating toxicity estimation and (c) integrating mutation data and mapping targets to known Protein-Protein Interaction (PPI) networks for providing further evidence for the significance of targets elucidated by the Probabilistic Target Inhibition Map framework. In addition, graduate students involved in this project will learn about translating fundamental research to commercially viable product by addressing technology gaps and being part of the intellectual property development process. The project engages Children?s Cancer Therapy Development Institute and University of Utah to provide experimental validation capabilities and commercialization expertise in this technology translation effort from research discovery towards commercial reality.", "AwardID" -> "1500234", "Institution" -> Entity["NSFInstitution", "TexasTechUniversity"], "Investigators" -> {Entity["NSFInvestigator", "RanadipPal"], Entity["NSFInvestigator", "GregJones"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500234&HistoricalAwards=false"], "KeywordTally" -> {{"drug", 6}, {"Inhibition", 5}, {"Probabilistic", 5}, {"project", 5}, {"Target", 5}, {"cancer", 4}, {"data", 4}, {"design", 4}, {"technology", 4}, {"therapy", 4}, {"toxicity", 4}, {"combination", 3}, {"combinations", 3}, {"existing", 3}, {"Map", 3}, {"personalized", 3}, {"research", 3}, {"()", 2}, {"addressing", 2}, {"alternative", 2}, {"application", 2}, {"approach", 2}, {"approaches", 2}, {"commercial", 2}, {"discovery", 2}, {"drugs", 2}, {"expected", 2}, {"framework", 2}, {"functional", 2}, {"gaps", 2}, {"incorporating", 2}, {"integrating", 2}, {"Maps", 2}, {"need", 2}, {"patients", 2}, {"provide", 2}, {"providing", 2}, {"recurrence", 2}, {"resulting", 2}, {"selection", 2}, {"significant", 2}, {"targets", 2}, {"therapies", 2}, {"towards", 2}, {"translating", 2}, {"treatment", 2}, {"validation", 2}}|>, "1500235" -> <|"AwardTitle" -> "Collaborative Research: Algebra and Algorithms, Structure and Complexity Theory", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[39486, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This project is a collaboration between mathematical researchers at five universities, including young mathematicians at the early stages of their careers, who are joining forces to tackle fundamental problems at the confluence of mathematical logic, algebra, and computer science. The overall goal is to deepen understanding about how to recognize the complexity of certain types of computational problems. The project focuses on a suite of mathematical problems whose solutions will yield new information about the complexity of Constraint Satisfaction Problems. These problems (CSP's) include scheduling problems, resource allocation problems, and problems reducible to solving systems of linear equations. CSP's are theoretically solvable, but some are not solvable efficiently. The research will be aimed at identifying a clear boundary between the tractable and intractable cases, and at providing efficient algorithms for solutions in the tractable cases. Many fundamental problems in mathematics and computer science can be formulated as CSP's, and progress here would have both practical and theoretical significance. A second component of the project investigates classical computational problems in algebra in order to determine whether they are algorithmically solvable. A third component of the project is the further development of the software UACalc, which is a proof assistant developed to handle computations involving algebraic structures.\n\nThe researchers shall work to decide the truth of the CSP Dichotomy Conjecture of Feder and Vardi, which states that every Constraint Satisfaction Problem with a finite template is solvable in polynomial time or is NP complete. They will further develop the algebraic approach to CSP's by refining knowledge about relations compatible with weak idempotent Maltsev conditions and about algebras with finitely related clones. A second goal of the project concerns the computable recognition of properties of finite algebras connected with the varieties they generate, such as whether a finite algebra with a finite residual bound is finitely axiomatizable, or whether a finite algebra can serve as the algebra of character values for a natural duality. One of the more tangible accomplishments of this project will be a broadening and strengthening of the applicability of the UACalc software. The agenda for this part of the project includes parallelizing the important subroutines, building in conjecture-testing and search features, adding further algorithms, and further developing the community of users and contributors.", "AwardID" -> "1500235", "Institution" -> Entity["NSFInstitution", "UniversityOfHawaii"], "Investigators" -> {Entity["NSFInvestigator", "RalphFreese"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500235&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 9}, {"project", 7}, {"algebra", 5}, {"finite", 5}, {"CSP's", 4}, {"solvable", 4}, {"mathematical", 3}, {"algebraic", 2}, {"algebras", 2}, {"algorithms", 2}, {"cases", 2}, {"complexity", 2}, {"component", 2}, {"computational", 2}, {"computer", 2}, {"Constraint", 2}, {"finitely", 2}, {"fundamental", 2}, {"goal", 2}, {"researchers", 2}, {"Satisfaction", 2}, {"science", 2}, {"second", 2}, {"software", 2}, {"solutions", 2}, {"tractable", 2}, {"UACalc", 2}}|>, "1500236" -> <|"AwardTitle" -> "PFI:AIR - TT: Developing an Engineering Prototype for Ultra-Low-Cost Blood Coagulation Diagnostics Using Paper-based Microfluidics", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating capillary-based paper microfluidics to fill the need for ultra-low-cost blood coagulation diagnostics. The diagnostic device is important for patients who receive blood thinner medication because of cardiovascular disease. These patients require constant blood coagulation analysis in order to monitor the efficacy of the anticoagulation medication. If the anticoagulant drug level is too low, the risk of blood clot formation is high. Conversely, if the drug level is too high severe bleeding (hemorrhage) can occur. Conventional hospital- or lab-based coagulation measurement is expensive and time consuming. The project will result in the development of engineering prototypes of simple paper-based diagnostic screening devices with several unique features: rapid indication of blood coagulation status; ease of use, with no other apparatus needed, thus allowing patient-operated home use; ultra-low-cost allowing one time use and preventing contamination; fast response time. These features provide significant cost savings compared to the leading competing blood coagulation portable measurement systems, thus greatly expanding the availability of point-of-care testing to currently underserved segment of the population. \n\nThis project addresses technology gaps in using blood samples with paper-based lateral flow assays (LFA) as it translates from research discovery toward commercial application. This includes specific design of test kits (LFA materials and cassettes) for use of small blood sample volume, enhanced sensitivity to coagulation conditions, low-cost manufacturability. A major consideration is the development of industrial-quality manufacturing processes, with particular consideration to reproducible fluid flow in the LFA nitrocellulose (NC) membranes. The geometrical definition of the NC membrane by mechanical cutting will be compared to a laser milling approach. In addition, personnel involved in this project (research assistant and research associate) will receive entrepreneurship and technology translation experiences through the Center for Entrepreneurship & Commercialization at the University of Cincinnati.\n\nThe project engages with industrial partners in this technology translation effort from research discovery toward commercial reality. Meridian Bioscience Inc. will provide guidance with overall prototype engineering, evaluation of product costs, regulatory requirements. Specific assistance with the design and optimization of the LFA unit will be provided by Diagnostic Consulting Network Inc.", "AwardID" -> "1500236", "Institution" -> Entity["NSFInstitution", "UniversityOfCincinnatiMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "GiovanniPauletti"], Entity["NSFInvestigator", "AndrewSteckl"], Entity["NSFInvestigator", "MichaelHegener"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500236&HistoricalAwards=false"], "KeywordTally" -> {{"blood", 8}, {"coagulation", 6}, {"project", 5}, {"LFA", 4}, {"research", 4}, {"use", 4}, {"technology", 3}, {"time", 3}, {"allowing", 2}, {"commercial", 2}, {"compared", 2}, {"consideration", 2}, {"design", 2}, {"development", 2}, {"diagnostic", 2}, {"discovery", 2}, {"drug", 2}, {"engineering", 2}, {"features", 2}, {"flow", 2}, {"high", 2}, {"Inc", 2}, {"level", 2}, {"measurement", 2}, {"medication", 2}, {"NC", 2}, {"paper-based", 2}, {"patients", 2}, {"provide", 2}, {"receive", 2}, {"translation", 2}, {"ultra-low-cost", 2}}|>, "1500237" -> <|"AwardTitle" -> "Topics in Number Theory", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2020, 6, 30}], "AwardAmount" -> Quantity[123156, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "This project involves research in the area of analytic number theory. An important class of problems in this area concerns L-functions, which encode arithmetic information. One example of an L-function is the Riemann zeta function, which controls the distribution of prime numbers. One of the investigator's main goals is to make progress on the value distribution and zeros of L-functions. Concurrently, one hopes to use such information to extract applications to problems in arithmetic. While these topics are of intrinsic interest in mathematics, progress in number theory has had important applications in cryptography and theoretical computer science. \n\nMore specifically, the investigator will continue his investigations on moments and value distribution of L-functions, extending in particular his recent work with Radziwill. The investigator will also continue work on multiplicative functions, in collaboration with Granville, Harper, and Koukoulopoulos. Besides these two main projects, the investigator will work with coauthors on various problems at the interface of analysis, number theory, and combinatorics, and continue his work in training graduate students in this area.", "AwardID" -> "1500237", "Institution" -> Entity["NSFInstitution", "StanfordUniversity"], "Investigators" -> {Entity["NSFInvestigator", "KannanSoundararajan"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500237&HistoricalAwards=false"], "KeywordTally" -> {{"work", 4}, {"area", 3}, {"continue", 3}, {"distribution", 3}, {"investigator", 3}, {"L-functions", 3}, {"number", 3}, {"problems", 3}, {"theory", 3}, {"applications", 2}, {"arithmetic", 2}, {"important", 2}, {"information", 2}, {"main", 2}, {"progress", 2}, {"value", 2}}|>, "1500238" -> <|"AwardTitle" -> "Collaborative Research: Heating the Solar Chromosphere Through Plasma Turbulence", "AwardEffectiveDate" -> DateObject[{2015, 7, 15}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[79950, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "The goal of this project is to provide a detailed verifiable explanation of the origin of the heating of the solar atmosphere. Most of the light reaching Earth originates at the 'surface' of the sun, a region called the photosphere. However, the regions of the solar atmosphere immediately above this surface, the solar chromosphere and corona, create most of the dangerous Ultraviolet (UV) and X-ray radiation. These regions also generate the solar wind, a stream of charged particles that pass the Earth at speeds in excess of 400km/s. Both the rapidly changing radiation and the solar wind create hazards for spacecraft, astronauts, and have a number of important terrestrial impacts. A long-standing mystery has prevented scientists from understanding and accurately modeling the chromosphere and corona. A short distance above the 'surface' of the sun, the solar atmosphere's temperature jumps up by a factor of two to three. The goal of this project is to provide an explanation of the origin of this heating. The project will also provide opportunities to recruit and train student researchers in plasma and solar physics, simulations, and modeling at the Boston University. Many of the Boston University PI's undergraduate research advisees, about half of whom are women, have continued on to graduate school. \n\nThis research will examine whether solar plasma flows emerging from the photosphere can transfer sufficient energy into turbulent plasma of the solar atmosphere, which, in turn, will heat the chromosphere sufficiently to explain whether the observed UV spectra originate there. It will also evaluate whether this mechanism can account for chromospheric spectral observations. This requires four linked research tasks: (1) solving for plasma drifts and fields when a convecting neutral gas pushes it across magnetic field lines; (2) analyzing the theory of streaming instabilities applicable to the collisional plasma found there; (3) performing a series of kinetic simulations to explore the nonlinear and thermal properties of the resulting turbulence; and (4) incorporating the resulting electron heating into a radiative transport code in order to evaluate its impact on chromospheric radiance. This research combines several research areas encompassed by the NSF/DOE Partnership in Basic Science and Engineering.", "AwardID" -> "1500238", "Institution" -> Entity["NSFInstitution", "NorthWestResearchAssociates,Incorporated"], "Investigators" -> {Entity["NSFInvestigator", "JohnFontenla"]}, "ProgramElements" -> {{"Code" -> "1242", "Text" -> "PLASMA PHYSICS"}}, "ProgramReferences" -> {{"Code" -> "1062", "Text" -> "BASIC PLASMA SCIENCE & ENGINEERING"}, {"Code" -> "7298", "Text" -> "COLLABORATIVE RESEARCH"}, {"Code" -> "8084", "Text" -> "CDS&E"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500238&HistoricalAwards=false"], "KeywordTally" -> {{"solar", 9}, {"plasma", 5}, {"research", 5}, {"atmosphere", 3}, {"chromosphere", 3}, {"heating", 3}, {"project", 3}, {"provide", 3}, {"surface", 3}, {"Boston", 2}, {"chromospheric", 2}, {"corona", 2}, {"create", 2}, {"Earth", 2}, {"evaluate", 2}, {"explanation", 2}, {"goal", 2}, {"modeling", 2}, {"origin", 2}, {"photosphere", 2}, {"radiation", 2}, {"regions", 2}, {"resulting", 2}, {"simulations", 2}, {"sun", 2}, {"University", 2}, {"UV", 2}, {"wind", 2}}|>, "1500240" -> <|"AwardTitle" -> "PFI:AIR - TT: Motionless MSM Micro-Pump", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2016, 12, 31}], "AwardAmount" -> Quantity[211955, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating a motionless magnetic shape memory (MSM) micropump to fill the need for draining bodily fluids and delivering dosages with small, lightweight, and highly reliable micro fluidic pumps. The motionless MSM micropump is important because it enables dosage of micro fluids at higher precision and greater reliability which will advance research in many areas of biology, chemistry, and medicine. For instance the motionless MSM micropump will drain fluids from organs such as brain and lung continuously without or with minimally invasive surgery as opposed to removal of such fluids through repeated surgical interventions which is the current state of the art. The project will result in a scalable prototype of a motionless MSM micropump. This motionless MSM micropump has the following unique features: it is lightweight, actuated contact-free, and can transport a large range of volumes from picoliter to milliliter. These features provide advantages such as reliability, precision, versatility, contact-free actuation, low power consumption when compared to the leading competing peristaltic pumps and syringe pumps in this market space. \n\nThis project addresses the following technology gaps as it translates from research discovery toward commercial application. The MSM pumping concept was demonstrated in 2012 at a pump actuated by a rotating permanent magnet. The micropump makes use of a magnetic shape memory alloy that shape-shifts in response to a dynamic magnetic field. Researchers will replace the rotating magnet with a set of electrical coils and a yoke turning the pump into a solid state device without moving parts. This will simplify the design, enable further miniaturization, and reduce weight. In addition, personnel involved in this project, including a post-doctoral engineering researcher and a MBA student, will receive experiences in innovation, product development and technology translation through combining a multifunctional, magneto-mechanical, smart material with electromagnetic field manipulation and through using a customer development process - namely the Lean Launchpad process - to build a sustainable business model around the motionless MSM micropump.\n\nThe project engages the animal hospital WestVet to establish clinical needs for a micropump in context with bodily fluid drainage in this technology translation effort from research discovery toward commercial reality. The project also engages Idaho TechHelp to connect the researchers with manufacturers in Idaho and the region.", "AwardID" -> "1500240", "Institution" -> Entity["NSFInstitution", "BoiseStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "KentNeupert"], Entity["NSFInvestigator", "PeterMullner"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "116E", "Text" -> "RESEARCH EXP FOR UNDERGRADS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9102", "Text" -> "WOMEN, MINORITY, DISABLED, NEC"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500240&HistoricalAwards=false"], "KeywordTally" -> {{"micropump", 7}, {"MSM", 7}, {"motionless", 6}, {"project", 6}, {"fluids", 4}, {"magnetic", 3}, {"pumps", 3}, {"research", 3}, {"technology", 3}, {"actuated", 2}, {"bodily", 2}, {"commercial", 2}, {"contact-free", 2}, {"development", 2}, {"discovery", 2}, {"engages", 2}, {"features", 2}, {"field", 2}, {"following", 2}, {"Idaho", 2}, {"lightweight", 2}, {"magnet", 2}, {"memory", 2}, {"micro", 2}, {"precision", 2}, {"process", 2}, {"pump", 2}, {"reliability", 2}, {"rotating", 2}, {"shape", 2}, {"state", 2}, {"translation", 2}}|>, "1500242" -> <|"AwardTitle" -> "PFI:AIR - TT: Biomimetic Composite for Segmental Bone Regeneration", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating a novel bone graft technology to fill the need for the reconstruction of large traumatic segmental bone defects. The innovative bone graft material is important in treating patients involved in vehicle accidents, cancer patients following tumor resection, soldiers involved in blast injuries, or children with congenital craniofacial injuries that require large amounts of bone graft to maintain continuity. The project will result in a prototype bone graft as an alternative to allograft or demineralized bone for reconstruction of segmental femur or tibia defects. The unique feature of this bone substitute technology is that the material mimics the natural structure and composition of dense cortical bone. This unique feature provides a safe, mechanically-stable, and resorbable graft that stimulates bone formation without eliciting an immune response and is ultimately displaced by the patient's own tissue. This results in a more sustainable healing solution when compared to the leading allograft products in the market. \n\nThis project addresses the gap in technology for an autologous bone graft in treating patients with large, traumatic segmental bone defects. A biomimetic approach is used to produce a scaffold structure similar to that of natural dense cortical bone in order to overcome the technological gap in insufficient strength as well as tunable resorption of the graft concurrent with bone formation. In this approach, osteoconductive microsheets are generated by nucleating calcium phosphate crystals on nanofibers functionalized with calcium-chelating peptides. Next, rigid, load-bearing scaffolds are generated by the wrapping and fusion of the microsheets into a cortical-bone-like cylindrical structure. Then, an array of microchannels are formed on the surface of the cylindrical structure by laser micro-drilling to form an interconnected network of Haversian- and Volkmann-like canals for tunable resorption and uniform nutrient transport in the scaffold. The biomimetic scaffold is loaded with bone morphogenetic protein-2 to produce a graft for recruitment of osteoprogenitor cells and regulation of stem cell fate toward bone formation. The outcome of this project is a non-immunogenic, mechanically-stable, conductive, and inductive bone graft ultimately displaced by the patient?s own tissue for a more sustainable healing solution. In addition, biomedical engineering undergraduates, doctoral students, and post-doctoral researchers involved in this project will receive training in entrepreneurship and technology translation through interviewing the people in different parts of the product ecosystem in collaboration with mentors at the Faber Entrepreneurship Center and the Office of Technology Commercialization at the University.", "AwardID" -> "1500242", "Institution" -> Entity["NSFInstitution", "UniversityOfSouthCarolinaAtColumbia"], "Investigators" -> {Entity["NSFInvestigator", "EsmaielJabbari"], Entity["NSFInvestigator", "ChadHardaway"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500242&HistoricalAwards=false"], "KeywordTally" -> {{"bone", 16}, {"graft", 9}, {"project", 5}, {"structure", 4}, {"technology", 4}, {"defects", 3}, {"formation", 3}, {"involved", 3}, {"large", 3}, {"patients", 3}, {"scaffold", 3}, {"segmental", 3}, {"allograft", 2}, {"approach", 2}, {"biomimetic", 2}, {"cortical", 2}, {"cylindrical", 2}, {"dense", 2}, {"displaced", 2}, {"feature", 2}, {"gap", 2}, {"generated", 2}, {"healing", 2}, {"injuries", 2}, {"material", 2}, {"mechanically-stable", 2}, {"microsheets", 2}, {"natural", 2}, {"produce", 2}, {"reconstruction", 2}, {"resorption", 2}, {"solution", 2}, {"sustainable", 2}, {"Technology", 2}, {"tissue", 2}, {"traumatic", 2}, {"treating", 2}, {"tunable", 2}, {"ultimately", 2}, {"unique", 2}}|>, "1500246" -> <|"AwardTitle" -> "PFI:AIR - TT: Commercializing an Intelligent Tutor for eLearning in Mathematics", "AwardEffectiveDate" -> DateObject[{2015, 5, 15}], "AwardExpirationDate" -> DateObject[{2016, 10, 31}], "AwardAmount" -> Quantity[199944, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation (TT) project addresses the high failure rate of K12 students to learn mathematics. This project focuses on technology translation of an intelligent online tutor, named MathSpring, which is important because it provides adaptive and personalized responses to students and teaches by matching the learning needs of individual students with effective teaching approaches. It applies theoretical understanding of cognitive, metacognitive and affective student characteristics to each tutor response. The MathSpring Tutor is also important because no online tutor today responds by analyzing both student knowledge and behavior. This PFI:AIR-TT project will result in a scale-up of the MathSpring Tutor and provide advantages in the marketplace by capitalizing on the general appeal of animation and humanoid characters that talk to students about the importance of perseverance and effort. The project will also provide low-cost, quality solutions for a wide range of students, adaptive tutoring based on student models, just-in-time verbal and animated interactions designed to move students away from boredom or disengagement, and the capability to select from among potentially 700 problems in the system. \n\nThese features of the MathSpring tutor provide improved performance, efficiency and efficacy when compared to classroom teaching or to the leading competing technology, primarily drill and practice problems, videos of lectures or games in this market space. The potential economic impact of translating this technology to the market place will positively contribute to the growth rate of eLearning within the next 5 years and to the U.S. competitiveness in the eLearning domain. Since the annual U.S. education expenditure for K-12 is approximately $625 billion, a large potential exists for making both a commercial and social impact in this space. Potential outcomes include: personalized tutors that guide students into their own zone or state of ?flow?; identification of target educational markets; and reaching any student with access to a computer and an Internet connection.\n\nThis PFI project addresses the following technology gaps as the software is translated from research discovery toward commercial application: identification of tutor responses that are effective for students in distress (e.g., bored, unmotivated); building sufficient content so the tutor can be used through an entire semester in Grades 5-9; and providing tools that enable teachers to select math problem based on the Common Core curriculum. The project work also includes hardening the tutor, porting it to two platforms (e.g., Android, IOS) and identifying consortia of schools (e.g., linked by geography, or pedagogy) for long-term partnerships. \n\nPersonnel involved in this project, e.g., graduate students and programmers, will receive innovation and technology translation experiences through efforts to identify paths through the idiosyncratic school procurement process and the communication of the efficacy studies arising from credible evaluation of MathSpring. The project engages CarneyLabs to guide commercial aspects of the translation and Virginia Advanced Studies Strategies (VASS), a non-profit company that works with the Virginia Department of Education (DoED), to provide a test environment in this technology translation effort from research discovery toward commercial reality.", "AwardID" -> "1500246", "Institution" -> Entity["NSFInstitution", "UniversityOfMassachusettsAmherst"], "Investigators" -> {Entity["NSFInvestigator", "BeverlyWoolf"], Entity["NSFInvestigator", "IvonArroyo"], Entity["NSFInvestigator", "PaulJesukiewicz"], Entity["NSFInvestigator", "JohnCarney"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500246&HistoricalAwards=false"], "KeywordTally" -> {{"students", 9}, {"project", 8}, {"tutor", 7}, {"technology", 6}, {"MathSpring", 5}, {"commercial", 4}, {"provide", 4}, {"student", 4}, {"translation", 4}, {"e.g", 3}, {"adaptive", 2}, {"addresses", 2}, {"based", 2}, {"discovery", 2}, {"effective", 2}, {"efficacy", 2}, {"effort", 2}, {"eLearning", 2}, {"guide", 2}, {"identification", 2}, {"impact", 2}, {"important", 2}, {"market", 2}, {"online", 2}, {"personalized", 2}, {"PFI", 2}, {"potential", 2}, {"problems", 2}, {"rate", 2}, {"research", 2}, {"responses", 2}, {"select", 2}, {"space", 2}, {"teaching", 2}, {"Tutor", 2}, {"U.S.", 2}, {"Virginia", 2}}|>, "1500249" -> <|"AwardTitle" -> "PFI:AIR - TT: Low Cost High Resolution 3D Scanning Technologies for 3D Printing", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[211999, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI:AIR Technology Translation project will leverage technologies developed under prior NSF projects to create advanced low-cost 3D scanners targeted at the flourishing consumer 3D printer market. Many low-cost desktop 3D printers are commercially available, but only a handful of low-cost desktop 3D scanners have been introduced in this market. Unfortunately, all these 3D scanners produce low quality 3D models as a result of intrinsic limitations of their technologies. Although the quality of existing low-cost 3D commercial (or home made) scanners is sufficient for hobbyists to replicate small objects using the current generation of personal 3D printers, the resolution of the low-cost desktop 3D scanners is not adequate for applications in art, entertainment, industrial inspection, reverse engineering, medicine, forensics, and in many other more advanced applications. Industrial 3D scanners, capable of producing high resolution 3D models, are available in the market, however they are at a price point one or two orders of magnitude higher, which makes them unsuitable for the high volume consumer 3D printer market, or even for some of the more advanced applications listed above. The 3D scanners to be developed in this project will be competitive in cost with existing low-cost desktop products, but able to produce 3D models of much higher quality, resulting in significant improvements over the state-of-the-art, with resulting competitive advantages.\n\nThe project will integrate proprietary technologies within a well designed user-friendly system, which will remove the most tedious steps through smart automation and advanced algorithm design: projector-camera calibration technology will enable the creation of a simple user-friendly semi-automatic calibration process, critical for high quality reconstruction; unsynchronized structured lighting technology will enable the project to leverage low cost hardware components manufactured in high volumes for the mobile market, and also to simplify the circuitry quite significantly; multi-frequency phase shifting technology will enable 3D scanning of objects made of optically challenging materials, such as polished metal and other anisotropic and translucent materials; smooth signed distance and non-convex hull surface reconstruction technologies will result in high fidelity multi-resolution polygon meshes. The project will also develop other unique image and geometry processing technologies to register multiple scans, to cleanup the reconstructed models, and to prepare the models for 3D printing.\n\nIn partnership with the Brown Program in Innovation Management and Entrepreneurship (PRIME), the project will analyze the market opportunities in a number of additional application domains, and will develop a broader marketing and commercialization strategy. A team of PRIME students will work to acquire an enhanced understanding of the identified market space, the market need, the competitive technologies; the potential impact of the proposed competitive innovation; necessary intellectual property protection, and licensing opportunities and freedom to operate issues. The students participating in this effort will acquire an enhanced understanding of innovation, technology commercialization and entrepreneurship through these experiences.", "AwardID" -> "1500249", "Institution" -> Entity["NSFInstitution", "BrownUniversity"], "Investigators" -> {Entity["NSFInvestigator", "GabrielTaubin"], Entity["NSFInvestigator", "AngusKingon"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "116E", "Text" -> "RESEARCH EXP FOR UNDERGRADS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500249&HistoricalAwards=false"], "KeywordTally" -> {{"3D", 16}, {"market", 8}, {"scanners", 7}, {"low-cost", 6}, {"project", 6}, {"technologies", 6}, {"high", 5}, {"models", 5}, {"advanced", 4}, {"competitive", 4}, {"desktop", 4}, {"quality", 4}, {"technology", 4}, {"applications", 3}, {"enable", 3}, {"acquire", 2}, {"available", 2}, {"calibration", 2}, {"commercialization", 2}, {"consumer", 2}, {"cost", 2}, {"develop", 2}, {"developed", 2}, {"enhanced", 2}, {"existing", 2}, {"higher", 2}, {"innovation", 2}, {"leverage", 2}, {"low", 2}, {"materials", 2}, {"objects", 2}, {"opportunities", 2}, {"PRIME", 2}, {"printer", 2}, {"printers", 2}, {"produce", 2}, {"reconstruction", 2}, {"resolution", 2}, {"result", 2}, {"resulting", 2}, {"students", 2}, {"understanding", 2}, {"user-friendly", 2}}|>, "1500253" -> <|"AwardTitle" -> "PFI:AIR - TT: Developing low-cost nanowire sensors based on a seed-mediated solution process", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[206000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating a novel, lower energy method of creating nanowires that will enable reliable, cost-effective and scalable manufacturing of nanowire sensors. Low-cost nanowire sensor technology is important because it has the potential to improve multiple types of detection systems, with impacts in disease detection, food safety, antiterrorism capabilities, higher crop yields (due to earlier detection of pathogens), and better protection for emergency responders and industrial plant workers (due to better chemical detection). The project will result in a proof-of-concept electrochemical nanosensor for gas/vapor sensing with the following unique features: 1) it will be based on a combined top-down and bottom-up nanomanufacturing method that directly deposits nanowires on micro-fabricated devices, 2) it will be fabricated via a room temperature process, 3) it will utilize a reversible synthesis process that may enable in-field regeneration and reuse, 4) it will have new or broadened sensor capabilities through a modular approach enabling combinatory synthesis of a wide range of novel organic nanowires, and 5) it will be compatible with flexible electronic architectures. These features will provide the following advantages: low-cost, scalable, reusable, modular, and applicable to a diverse range of chemicals as compared to other competing sensor technologies in this market space.\n\nNanowires have been applied to sensing for over 10 years but few nanowire sensors have reached the market. The major barriers are the complexity of manufacturing and difficulty in connecting nanowires in microelectronic devices. In current competing technologies, nanowires need to be aligned and placed at precise locations and orientations on the patterned substrates, a complex process to scale up. This new technology synthesizes nanowires directly on the metal substrates by using the metal micro- and nanopattern as nucleation points to grow the nanowires. It is based on seed-mediated nucleation research. When a nanoparticle is used as a seed, the high curvature of the seed imposes unsustainable strain energy on the nucleated crystal at the crystal/seed interface and results in a nanowire crystal. In addition, a graduate student involved in this project will gain technology translation experience through exposure to business methodologies, access to technology transfer networks, and a deeper engagement in the university technology transfer process.\n\nThe project engages a serial entrepreneur with prior experience in nanotechnology ventures to guide technology transfer and commercialization activities, and an established technology-enabling company to augment research capability in this technology translation effort from research discovery toward commercial reality.", "AwardID" -> "1500253", "Institution" -> Entity["NSFInstitution", "WayneStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "NicholasCucinelli"], Entity["NSFInvestigator", "GuangzhaoMao"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "116E", "Text" -> "RESEARCH EXP FOR UNDERGRADS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500253&HistoricalAwards=false"], "KeywordTally" -> {{"nanowires", 7}, {"technology", 7}, {"detection", 4}, {"nanowire", 4}, {"project", 4}, {"crystal", 3}, {"process", 3}, {"research", 3}, {"seed", 3}, {"sensor", 3}, {"transfer", 3}, {"based", 2}, {"better", 2}, {"capabilities", 2}, {"competing", 2}, {"devices", 2}, {"directly", 2}, {"due", 2}, {"enable", 2}, {"energy", 2}, {"experience", 2}, {"features", 2}, {"following", 2}, {"manufacturing", 2}, {"market", 2}, {"metal", 2}, {"method", 2}, {"modular", 2}, {"new", 2}, {"novel", 2}, {"nucleation", 2}, {"range", 2}, {"scalable", 2}, {"sensing", 2}, {"sensors", 2}, {"substrates", 2}, {"synthesis", 2}, {"technologies", 2}, {"translation", 2}}|>, "1500254" -> <|"AwardTitle" -> "Collaborative Research: Algebra and Algorithms, Structure and Complexity Theory", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[144199, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This project is a collaboration between mathematical researchers at five universities, including young mathematicians at the early stages of their careers, who are joining forces to tackle fundamental problems at the confluence of mathematical logic, algebra, and computer science. The overall goal is to deepen understanding about how to recognize the complexity of certain types of computational problems. The project focuses on a suite of mathematical problems whose solutions will yield new information about the complexity of Constraint Satisfaction Problems. These problems (CSP's) include scheduling problems, resource allocation problems, and problems reducible to solving systems of linear equations. CSP's are theoretically solvable, but some are not solvable efficiently. The research will be aimed at identifying a clear boundary between the tractable and intractable cases, and at providing efficient algorithms for solutions in the tractable cases. Many fundamental problems in mathematics and computer science can be formulated as CSP's, and progress here would have both practical and theoretical significance. A second component of the project investigates classical computational problems in algebra in order to determine whether they are algorithmically solvable. A third component of the project is the further development of the software UACalc, which is a proof assistant developed to handle computations involving algebraic structures.\n\nThe researchers shall work to decide the truth of the CSP Dichotomy Conjecture of Feder and Vardi, which states that every Constraint Satisfaction Problem with a finite template is solvable in polynomial time or is NP complete. They will further develop the algebraic approach to CSP's by refining knowledge about relations compatible with weak idempotent Maltsev conditions and about algebras with finitely related clones. A second goal of the project concerns the computable recognition of properties of finite algebras connected with the varieties they generate, such as whether a finite algebra with a finite residual bound is finitely axiomatizable, or whether a finite algebra can serve as the algebra of character values for a natural duality. One of the more tangible accomplishments of this project will be a broadening and strengthening of the applicability of the UACalc software. The agenda for this part of the project includes parallelizing the important subroutines, building in conjecture-testing and search features, adding further algorithms, and further developing the community of users and contributors.", "AwardID" -> "1500254", "Institution" -> Entity["NSFInstitution", "UniversityOfColoradoAtBoulder"], "Investigators" -> {Entity["NSFInvestigator", "PeterMayr"], Entity["NSFInvestigator", "AgnesSzendrei"], Entity["NSFInvestigator", "KeithKearnes"]}, "ProgramElements" -> {{"Code" -> "1253", "Text" -> "OFFICE OF MULTIDISCIPLINARY AC"}, {"Code" -> "1268", "Text" -> "FOUNDATIONS"}, {"Code" -> "1271", "Text" -> "COMPUTATIONAL MATHEMATICS"}, {"Code" -> "2878", "Text" -> "SPECIAL PROJECTS - CCF"}}, "ProgramReferences" -> {{"Code" -> "7433", "Text" -> "CyberInfra Frmwrk 21st (CIF21)"}, {"Code" -> "7933", "Text" -> "NUM, SYMBOL, & ALGEBRA COMPUT"}, {"Code" -> "9263", "Text" -> "COMPUTATIONAL SCIENCE & ENGING"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500254&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 9}, {"project", 7}, {"algebra", 5}, {"finite", 5}, {"CSP's", 4}, {"solvable", 4}, {"mathematical", 3}, {"algebraic", 2}, {"algebras", 2}, {"algorithms", 2}, {"cases", 2}, {"complexity", 2}, {"component", 2}, {"computational", 2}, {"computer", 2}, {"Constraint", 2}, {"finitely", 2}, {"fundamental", 2}, {"goal", 2}, {"researchers", 2}, {"Satisfaction", 2}, {"science", 2}, {"second", 2}, {"software", 2}, {"solutions", 2}, {"tractable", 2}, {"UACalc", 2}}|>, "1500256" -> <|"AwardTitle" -> "PFI:AIR - TT: Low cost method for harvesting algal biomass from dilute cultures", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[199997, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on improving and demonstrating the recovery of algal biomass from dilute growth cultures with minimal cost and energy input. This project has the potential to lead to economical use of alternative fuels derived from algal biomass. The lack of low-cost technologies for harvesting algae is currently a major bottleneck in the commercial production of fuels from microalgae. When cultivated in open raceway ponds, microalgae concentrations are very low - typically 0.1%. Stimuli-sensitive hydrogels are capable of selectively soaking up large quantities of culture media (without absorbing microalgae cells), thus efficiently increasing concentrations of the microalgal cultures, leading to a more efficient recovery of the microalgal cells. This allows separation of solid cells from liquid media in a cost- and energy-efficient manner and without use of additional chemicals as compared to competing chemical flocculation methods. In addition, the absorbed liquid in the hydrogel can subsequently be released easily through small increases in hydrogel temperature (from ambient to 35°C). The recovered (de-swelled) hydrogels, as well as the growth medium, can then be reused over multiple cycles to create a sustainable algae harvesting process through effective recycling of water and un-utilized water-soluble nutrients.\n\nThis project addresses the following technology gaps as it translates from research discovery toward commercial application: (i) continuous hydrogel harvesting in a scalable prototype that minimizes exposure of the gel to mechanical attrition and preserves gel longevity; (ii) use of waste flue gases to de-swell hydrogels through heat integration, (iii) establishes benchmarks for harvesting efficiency, highest culture concentrations achievable, quality of harvested product, and hydrogel stability during prolonged-use. In addition, undergraduate and graduate students involved in this project will receive innovation and technology translation experiences through design, development and testing of hydrogel-based algae harvesting prototypes.", "AwardID" -> "1500256", "Institution" -> Entity["NSFInstitution", "UniversityOfToledo"], "Investigators" -> {Entity["NSFInvestigator", "SridharViamajala"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500256&HistoricalAwards=false"], "KeywordTally" -> {{"harvesting", 5}, {"hydrogel", 4}, {"project", 4}, {"algae", 3}, {"cells", 3}, {"concentrations", 3}, {"hydrogels", 3}, {"microalgae", 3}, {"use", 3}, {"addition", 2}, {"algal", 2}, {"biomass", 2}, {"commercial", 2}, {"cost", 2}, {"culture", 2}, {"cultures", 2}, {"fuels", 2}, {"gel", 2}, {"growth", 2}, {"liquid", 2}, {"media", 2}, {"microalgal", 2}, {"recovery", 2}, {"technology", 2}}|>, "1500261" -> <|"AwardTitle" -> "PFI:AIR - TT: Development of Tools and Methods for Extended Maturity Analysis of Concrete", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating a microscale sensor of water stress and temperature for real-time monitoring of the chemical state within concrete during curing, and for refined predictions of the concrete's mechanical properties. The HydroT sensor of water status and temperature, and the Extended Maturity Analysis that it will enable, are important because they will allow for improved control of the properties of concrete during curing. Improper curing of concrete structures can cause stress that may lead to cracking and ultimate failure. Real-time sensing and monitoring of concrete curing will lead to improved functionality, increased lifetime, and a reduction in the global use of this energy-intensive material. \n\nThe project will result in prototypes of the HydroT sensor, initial development of Extended Maturity Methods using these sensors in concrete curing, and an improved understanding of the priority markets for the commercialization of this technology. The HydroT sensor has the following unique features: 1) unprecedented sensitivity for the measurement of water stress in the range that is relevant in concrete. This capability will allow for water status to be incorporated, for the first time, into methods of tracking and controlling concrete properties during construction. 2) Integration of water and temperature sensing using microfabrication techniques. This approach will allow for simple, low-cost scaled-up and production by leveraging the existing capabilities of microfabrication foundries. 3) Small format and simple integration with electronics and communication. These characteristics will make the barrier for adoption by industry low. Taken together, these features mean that the HydroT technology will provide the concrete industry an important new functionality (sensing of water status) in a device that can replace the temperature probes used in conventional Maturity Analysis with similar costs and technical complexity. \n\nTo translate the HydroT Probe and Extended Maturity Analysis toward commercial application, the team will pursue advances in the understanding and technical approaches on both hardware and application fronts. These developments will involve fundamental advances in the ability to manipulate the properties of critical materials such as the porous membrane and deeper understanding of the coupling of moisture and temperature in defining maturation in important classes of concrete. Additionally, the team will pursue a deeper understanding of the market, competitors, and potential partners for manufacturing and distribution. Throughout, the team will aim to reinforce its intellectual property position and to build a core group of entrepreneurs and technical staff to carry the project into a successful start-up company. As part of the project, the personnel involved - undergraduates, graduates, and post-docs - will gain experience in innovation, entrepreneurship, and technology translation through participation in the patent application process with Cornell's technology transfer office and activities such as Cornell's Pre-Seed Workshop and technology accelerator program, eLabs.", "AwardID" -> "1500261", "Institution" -> Entity["NSFInstitution", "CornellUniversity"], "Investigators" -> {Entity["NSFInvestigator", "KennethHover"], Entity["NSFInvestigator", "AbrahamStroock"], Entity["NSFInvestigator", "ChaoKoi"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500261&HistoricalAwards=false"], "KeywordTally" -> {{"concrete", 9}, {"water", 6}, {"curing", 5}, {"HydroT", 5}, {"technology", 5}, {"temperature", 5}, {"Maturity", 4}, {"project", 4}, {"properties", 4}, {"sensor", 4}, {"understanding", 4}, {"allow", 3}, {"Analysis", 3}, {"application", 3}, {"Extended", 3}, {"important", 3}, {"improved", 3}, {"sensing", 3}, {"status", 3}, {"stress", 3}, {"team", 3}, {"technical", 3}, {"advances", 2}, {"br/>

", 2}, {"Cornell's", 2}, {"deeper", 2}, {"features", 2}, {"functionality", 2}, {"industry", 2}, {"lead", 2}, {"microfabrication", 2}, {"monitoring", 2}, {"pursue", 2}, {"simple", 2}, {"using", 2}}|>, "1500262" -> <|"AwardTitle" -> "Iterated Fourier Series and Integrals", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[160752, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "A fundamental question in mathematical physics is the so-called planar N-body problem. In broad terms, it asks one to analyze the orbits of several particles/bodies that initially move independently and circularly around a fixed point in a plane, and then start to interact with each other, possibly in a nonlinear fashion. The basic question of interest is the following: With the passage of time, under what circumstances do the orbits of these particles/bodies remain bounded? Examples include the Solar System, where the planets are moving around the Sun, and the (planar) galaxies, where the stars move around a black hole. Recently, it has been discovered that there are deep connections between this problem and the field of harmonic analysis, and the present project aims to explore and understand these connections more quantitatively.\n\nThere are several extremely interesting nonlinear operators that one needs to understand from a harmonic analysis point of view in order to give meaningful answers to the question above, at least in some particular situations. Some of them include Carleson-type maximal operators associated to iterated Fourier integrals that are generated by combinatorial trees. The complexity of these trees is naturally linked to the complexity of the nonlinear interactions between the particles/bodies. For instance, quadratic interactions generate binary trees, cubic interactions corresponds to ternary trees, and so on. In particular, the simplest case of 1-ary trees is the one that comes from linear interactions, and it was studied by the principal investigator in collaboration with Tao and Thiele some years ago. This is the case that generated the standard iterated Fourier series and integrals. The aim of this project is to develop the necessary analytical tools to understand the boundedness properties of such nonlinear operators.", "AwardID" -> "1500262", "Institution" -> Entity["NSFInstitution", "CornellUniversity"], "Investigators" -> {Entity["NSFInvestigator", "CamilMuscalu"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500262&HistoricalAwards=false"], "KeywordTally" -> {{"trees", 5}, {"interactions", 4}, {"nonlinear", 4}, {"bodies", 3}, {"operators", 3}, {"particles", 3}, {"question", 3}, {"understand", 3}, {"analysis", 2}, {"case", 2}, {"complexity", 2}, {"connections", 2}, {"Fourier", 2}, {"generated", 2}, {"harmonic", 2}, {"include", 2}, {"integrals", 2}, {"iterated", 2}, {"move", 2}, {"orbits", 2}, {"particular", 2}, {"planar", 2}, {"point", 2}, {"problem", 2}, {"project", 2}}|>, "1500264" -> <|"AwardTitle" -> "Local Cohomology and Related Questions", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[60000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "This project is in commutative algebra and algebraic geometry, fields where solution sets of polynomial equations are studied. These areas have many applications in other areas of mathematics and in other disciplines. The project is concerned with questions in local cohomology, a powerful tool used in commutative algebra, and connections with several other areas of mathematics. The discovery of a connection between two different areas of mathematics holds a potential for enriching both of them by making available new sets of techniques for attacking old problems. Advising students, mentoring postdocs, giving invited talks, and organizing a conference on D-modules in commutative algebra will also be part of this project. \n\nA large part of the investigator's research on local cohomology over the last twenty years has been devoted to the study of a number of striking connections with several quite diverse areas of mathematics. For example, local cohomology provides a way of proving otherwise inaccessible results on the topology of algebraic varieties, while D-modules provide a way of proving otherwise inaccessible finiteness properties of local cohomology modules. While considerable progress on this circle of ideas has been made, many open questions remain. The project is aimed at a better understanding of a number of interrelated problems such as the structure and algorithmic computation of local cohomology modules, Lyubeznik numbers, De Rham homology and cohomology of algebraic varieties, the direct summand conjecture (via the absolute integral closure of a local domain in mixed characteristic), and tight closure. Local cohomology is the common thread that runs through all these problems and connects them to each other. The principal methods to be employed are the use of D-modules and F-modules.", "AwardID" -> "1500264", "Institution" -> Entity["NSFInstitution", "UniversityOfMinnesota-TwinCities"], "Investigators" -> {Entity["NSFInvestigator", "GennadyLyubeznik"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500264&HistoricalAwards=false"], "KeywordTally" -> {{"cohomology", 7}, {"local", 6}, {"areas", 5}, {"mathematics", 4}, {"project", 4}, {"algebra", 3}, {"algebraic", 3}, {"commutative", 3}, {"D-modules", 3}, {"problems", 3}, {"closure", 2}, {"connections", 2}, {"inaccessible", 2}, {"modules", 2}, {"number", 2}, {"otherwise", 2}, {"proving", 2}, {"questions", 2}, {"sets", 2}, {"varieties", 2}, {"way", 2}}|>, "1500267" -> <|"AwardTitle" -> "EAGER: Collaborative Research: Conceptualizing sustained environmental information management in the landscape of current and emerging eco-informatics infrastructure", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 3, 31}], "AwardAmount" -> Quantity[17003, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08080000", "ProgramOfficer" -> "Peter H. McCartney", "Abstract" -> "The data generated by environmental research are highly valuable, not only because of the cost of research but also because they are irreplaceable and needed for understanding change. A major challenge for all research entities is the management of this digital asset and associated information for maintaining its value. This challenge is complex in nature, covering not only the collection and storage of data, but also the creation of relevant (and sufficient) information about the data (metadata), such that they can be re-used broadly. Several environmental data repositories and data management approaches have been developed over the past few years. It is now time to seek input from researchers in the role of data authors and data re-users and data managers, to expansively explore the current operating environment, potential collaboration opportunities, efficiencies of scale, and future community needs for this challenge to be addressed effectively. An initial workshop will allow these stakeholders to share their expertise, experience and future requirements with their colleagues. The output from this initial exercise will then feed into a second session, which will result in strategic recommendations detailing the activities needed to create a collaborative and efficient data management infrastructure capable of supporting future environmental science research endeavors. \n\nMost current environmental data repositories fulfill specific needs or objectives, i.e., archiving and disseminating data from a project, network of research sites, institution, a specific funding source, or to accompany paper publications. Envisioning a sustained Scientific Data Infrastructure (SDI), and with the goal of providing high quality data to researchers, policy makers and the general public, this project concentrates on data repositories and current curation practices as an integral part of this vision. Within this scope and in the context of environmental research data management, original goals and objectives of single repositories will be re-evaluated, efficiencies of scale identified, a cost-benefit analyses for some centralized services attempted, and new, sustainable collaborations conceptualized. Specifically, data curators from a range of environmental research fields, data aggregators, tool developers, computer scientists and environmental scientists (both data providers and users) will be brought together for an informed dialog which draws on this broad collective experience. A preliminary information-gathering phase will describe the characteristics of each repository to inform the discussion at two subsequent community workshops. The first workshop will identify new collaboration and curation strategies that also cater to the currently underserved single investigators and move environmental data from \"available\" to \"usable\", in order to accelerate scientific inquiry. The second workshop will examine these strategies further, and develop one or more alternative, community-vetted roadmaps for research information management with the goal of more efficiently and sustainably utilizing NSF investments. In summary, these workshops will produce a strategic implementation plan outlining one or more options for a sustained environmental data management infrastructure capable of accelerating scientific inquiry, serve all contributing investigators (data producers) and provide the basis for education and outreach activities in a cost effective approach. Data management needs are fairly well understood. Organizational, personnel and management structures are not. Hence, the plan will focus on these challenges while also considering workforce development. A website for this project will be established at http://sedicollaborative.org.", "AwardID" -> "1500267", "Institution" -> Entity["NSFInstitution", "ArizonaStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "PhilipTarrant"]}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Div Of Biological Infrastructure", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500267&HistoricalAwards=false"], "KeywordTally" -> {{"data", 20}, {"environmental", 9}, {"management", 8}, {"research", 8}, {"repositories", 4}, {"challenge", 3}, {"current", 3}, {"future", 3}, {"information", 3}, {"needs", 3}, {"project", 3}, {"workshop", 3}, {"activities", 2}, {"capable", 2}, {"collaboration", 2}, {"community", 2}, {"cost", 2}, {"curation", 2}, {"Data", 2}, {"efficiencies", 2}, {"experience", 2}, {"goal", 2}, {"infrastructure", 2}, {"initial", 2}, {"inquiry", 2}, {"investigators", 2}, {"needed", 2}, {"new", 2}, {"objectives", 2}, {"plan", 2}, {"researchers", 2}, {"scale", 2}, {"scientific", 2}, {"scientists", 2}, {"second", 2}, {"single", 2}, {"specific", 2}, {"strategic", 2}, {"strategies", 2}, {"sustained", 2}, {"workshops", 2}}|>, "1500271" -> <|"AwardTitle" -> "PFI:AIR - TT: High-Rate High-Powered Pulsed Magnetron Sputtering (HPPMS) Prototype Development", "AwardEffectiveDate" -> DateObject[{2015, 4, 15}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[222000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating a new magnetic field configuration used in physical vapor deposition to large-scale rectangular cathodes used for many applications. The TriPAC magnetic arrangement is important because it allows a new type of high-power pulsed magnetron sputtering (HPPMS) to achieve the same deposition rates as conventional sputtering sources. The project will result in a higher quality coatings (less stress, higher density, better adhesion) broadly impacting many different industries and research areas- from consumer items (razor blades) to energy production (photovoltaics) to semiconductors (displays) to decorative coatings (bathroom faucets). The advantage of the innovation is the way the new magnetic field is generated, using only permanent magnets, and the whole assembly can fit into the standard design of magnetrons where conventional magnet assemblies are positioned. These features will allow easy adoption in the market place and will allow HPPMS to be used in a cost-effective manner compared to the standard magnet packs currently in use. \n\nThis project addresses the following technology gaps as it translates from research discovery toward commercial application. This new magnetic field topology works better than current magnetic fields because it allows plasma to expand further from cathode and provides a less steep potential drop. With this new electric field orientation, ionized sputtered material is more directed towards substrate to be coated and utilized for film deposition in larger quantities than with the conventional magnetic field configuration. The average incident atom energy is also increased, further improving film densification and making the HPPMS technique more attractive for thin-film coatings. In addition, personnel involved in this project, undergraduate, graduate and post-doctoral students, will receive technology translation experiences through seeing this invention turn into a commercial product.\n\nThe project engages Starfire Industries Inc., a small business specializing in bridging the \"valley of death\" to take the design which works in the research lab and turn it into a manufacturable product, and the Kurt J. Lesker Company - a large leading firm in this area. This partnership will enable the technology translation effort from a research discovery toward a commercial reality.", "AwardID" -> "1500271", "Institution" -> Entity["NSFInstitution", "UniversityOfIllinoisAtUrbana-Champaign"], "Investigators" -> {Entity["NSFInvestigator", "DavidRuzic"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "116E", "Text" -> "RESEARCH EXP FOR UNDERGRADS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "8808", "Text" -> "Veterans Research Supplements"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500271&HistoricalAwards=false"], "KeywordTally" -> {{"magnetic", 6}, {"field", 5}, {"new", 5}, {"project", 5}, {"research", 4}, {"coatings", 3}, {"commercial", 3}, {"conventional", 3}, {"deposition", 3}, {"HPPMS", 3}, {"technology", 3}, {"used", 3}, {"allow", 2}, {"allows", 2}, {"better", 2}, {"configuration", 2}, {"design", 2}, {"discovery", 2}, {"energy", 2}, {"film", 2}, {"higher", 2}, {"magnet", 2}, {"sputtering", 2}, {"standard", 2}, {"translation", 2}, {"turn", 2}, {"works", 2}}|>, "1500273" -> <|"AwardTitle" -> "PFI:AIR - TT: High yield production of furans from biomass hydrolysates using a hybrid enzyme- and chemo-catalytic technology", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[222000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on a transformative technology for converting biomass to platform chemicals (furans) that would replace petroleum-derived feedstocks for fuel and chemical production. These furans serve as building blocks for a variety of other chemicals and intermediates that are necessary in industry. A process that allows them to be economically produced from renewable resources (e.g. biomass) instead of petroleum-based technologies would result in reduced dependence on fossil fuels, reduced emission of greenhouse gases, and minimal environmental impact. \n\nThe project will result in a proof-of-concept development, demonstration, and evaluation of an integrated hybrid enzyme-and chemo-catalytic technology for high-yield production of furans from biomass sugars. When compared to competing processes that rely on inefficient water-based reaction media, the technology has several distinct advantages. It provides a cohesive pathway to efficiently transfer biomass sugars into a non-aqueous reaction medium; produces the furan product in high yield; and isolates the furan for downstream processing, all with low energy input and recycling of process streams. \n\nThis project addresses the following technology gaps as it translates from research discovery toward commercial application: (1) the design, construction, and testing of a scalable process configuration that allows transition from bench to larger scale; (2) the collection of metrics for the prolonged operation of the integrated process; (3) the assessment of the process economics and environmental impacts; and (4) the evaluation of the integrated process with diverse biomass feedstocks and their upstream pretreatment/saccharification methods. In addition, personnel involved in this project, namely undergraduate and graduate students, will receive entrepreneurship and innovation experiences through new interdisciplinary initiatives developed at The University of Toledo based on the Lean LaunchPad approach.", "AwardID" -> "1500273", "Institution" -> Entity["NSFInstitution", "UniversityOfToledo"], "Investigators" -> {Entity["NSFInvestigator", "PatriciaRelue"], Entity["NSFInvestigator", "SasidharVaranasi"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "115E", "Text" -> "RESEARCH EXP FOR TEACHERS"}, {"Code" -> "116E", "Text" -> "RESEARCH EXP FOR UNDERGRADS"}, {"Code" -> "7218", "Text" -> "RET SUPPLEMENTS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9102", "Text" -> "WOMEN, MINORITY, DISABLED, NEC"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}, {"Code" -> "9177", "Text" -> "ELEMENTARY/SECONDARY EDUCATION"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500273&HistoricalAwards=false"], "KeywordTally" -> {{"process", 6}, {"biomass", 5}, {"project", 4}, {"technology", 4}, {"furans", 3}, {"integrated", 3}, {"allows", 2}, {"br/>

", 2}, {"chemicals", 2}, {"environmental", 2}, {"evaluation", 2}, {"feedstocks", 2}, {"furan", 2}, {"production", 2}, {"reaction", 2}, {"reduced", 2}, {"result", 2}, {"sugars", 2}}|>, "1500275" -> <|"AwardTitle" -> "New Strategy for Encapsulating Integral Membrane Proteins", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[300000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03070000", "ProgramOfficer" -> "Aleksandr Simonian", "Abstract" -> "Non-Technical: The PIs goal is to provide a strategy so that the majority of integral membrane proteins (IMPs) could be routinely encapsulated in the nanometer-sized pores of gels for drug discovery, and biotechnology, and energy generation. IMPs are nanometer-size biological workhorses that produce energy, serve as receptors, channels, transporters, and enzymes, when they are embedded in biological membrane hosts. Similarly, nanoporous gels and glasses are mainstays of modern technology because of their unique photochemical, optical, and catalytic properties. PIs IMP-containing bio-functional gels will combine these unique functionalities: e.g. the gel (for solar energy capture) and the IMP for energy absorption from a broader spectrum of wavelengths. They will study nanolipoprotein particles (NLPs) as the biological membrane hosts of IMPs entrapped in inorganic and organic nanoporous gels. NLPs are disc-shaped 10-25 nanometer-sized lipid bilayer patches stabilized by a belt of scaffold proteins. The NLP approach represents a major breakthrough because NLPs fit precisely into the 5-50 nanometer-sized pores of the gels and NLPs serve as a robust host for any IMP so that all components remain functional. On the training side, engineering undergraduates and graduate students working on this project will gain valuable experience that will prepare them for new careers that integrate materials science with biotechnology. Following previous success the PIs will organize a second international workshop \"Biomembrane Frontiers: Nanostructures, Models, and the Design of Life: II\". Further, they will publish a Tutorial Review on \"Creating and Characterizing Biomembrane/Materials Interfaces\". \n\n\nTechnical: Integral membrane proteins (IMPs) require a lipid membrane host and carry out a number of useful biological functions that could be harnessed by routine encapsulation in mesoporous sol-gel materials. The PIs will study nanolipoprotein particles (NLPs) as the biological membrane hosts of IMPs entrapped in inorganic and organic mesoporous sol-gels. NLPs are soluble discoidal 10-25 nm-sized particles comprised of a lipid bilayer patch stabilized by a belt of apolipoprotein scaffold proteins that can be formed through in vitro self-assembly. NLPs fit precisely into the 5-50 nm-sized pores of the gels and NLPs serve as robust hosts for IMPs, therefore all components may retain their structures and functions. Exploration of the parameters of nanoscale confinement and chemical environment in relation to dynamics, structure, and function of the NLP and IMP-NLP are important from a scientific standpoint as well as toward imagining and optimizing any future applications. Characterization of these parameters will take place with integrated studies employing state-of-the-art dynamic TEM, electron paramagnetic resonance, NMR, circular dichroism, and fluorimetry. Materials Science and Chemical Engineering undergraduates and graduate students working on this project will receive valuable interdisciplinary training in new cell biological and bioengineering techniques, i.e. cell free expression, in the context of production of a functional biocomposite sol-gel materials. The PIs will organize an international workshop, \"Biomembrane Frontiers: Nanostructures, Models, and the Design of Life: II\" and publish an Instructional Review on \"Creating and Characterizing Biomembrane/Materials Interfaces\". In the education arena, PIs will provide special topical freshman seminars on Biomaterials.", "AwardID" -> "1500275", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Davis"], "Investigators" -> {Entity["NSFInvestigator", "SubhashRisbud"], Entity["NSFInvestigator", "MarjorieLongo"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Materials Research", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500275&HistoricalAwards=false"], "KeywordTally" -> {{"NLPs", 8}, {"biological", 6}, {"gels", 6}, {"IMPs", 6}, {"membrane", 6}, {"PIs", 6}, {"Biomembrane", 4}, {"energy", 4}, {"hosts", 4}, {"proteins", 4}, {"lipid", 3}, {"materials", 3}, {"Materials", 3}, {"nanometer-sized", 3}, {"particles", 3}, {"pores", 3}, {"serve", 3}, {"10-25", 2}, {"5-50", 2}, {"belt", 2}, {"bilayer", 2}, {"biotechnology", 2}, {"cell", 2}, {"Characterizing", 2}, {"components", 2}, {"Creating", 2}, {"Design", 2}, {"entrapped", 2}, {"fit", 2}, {"Frontiers", 2}, {"functional", 2}, {"functions", 2}, {"graduate", 2}, {"host", 2}, {"II", 2}, {"IMP", 2}, {"inorganic", 2}, {"Interfaces", 2}, {"international", 2}, {"Life", 2}, {"mesoporous", 2}, {"Models", 2}, {"nanolipoprotein", 2}, {"nanoporous", 2}, {"Nanostructures", 2}, {"new", 2}, {"NLP", 2}, {"nm-sized", 2}, {"organic", 2}, {"organize", 2}, {"parameters", 2}, {"precisely", 2}, {"project", 2}, {"provide", 2}, {"publish", 2}, {"Review", 2}, {"robust", 2}, {"scaffold", 2}, {"sol-gel", 2}, {"stabilized", 2}, {"students", 2}, {"study", 2}, {"training", 2}, {"undergraduates", 2}, {"unique", 2}, {"valuable", 2}, {"working", 2}, {"workshop", 2}}|>, "1500284" -> <|"AwardTitle" -> "California LSAMP Bridge to the Doctorate Program at the University of California-Irvine (2015-2017)", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Tasha Inniss", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the Science, Technology, Engineering, and Mathematics (STEM) workforce through the development of highly competitive students from groups historically underrepresented in STEM disciplines: African-Americans, Alaska Natives, American Indians, Hispanic Americans, Native Hawaiians, and Native Pacific Islanders. The goal of the LSAMP Bridge to the Doctorate (BD) Activity is to increase the quantity and quality of STEM graduate students from underrepresented populations, with emphasis on Ph.D. matriculation and completion. BD programs implemented in the nation's institutions of higher education contribute to addressing one of the objectives in NSF's 2014-2018 Strategic Plan, namely to \"integrate education and research to support development of a diverse STEM workforce with cutting-edge capabilities.\" For the U.S. to remain globally competitive, it is vital that it taps into the talent of all its citizens and provides exceptional educational preparedness in STEM areas that underpin the knowledge-based economy. The University of California-Irvine (UCI), lead institution of the California LSAMP (CAMP), will serve as the host site for the 2015-2017 cohort of BD Fellows. The BD Program at UCI will employ creative strategies and best practices for recruitment and retention of diverse graduate student researchers through completion of the Ph.D. The efforts to invest in doctoral students underrepresented in STEM should result in the production of well-trained scientists and engineers who would support NSF's Mission to promote the progress of science. Ultimately, the CAMP BD Program will positively impact diversity and inclusion in the national scientific and engineering workforce, thereby ensuring our nation's future prosperity and competitiveness.\n\nThe BD Program at UCI will enhance the diversity of STEM graduate education on the Irvine campus by recruiting, enrolling, training, and graduating a cohort of 12 talented doctoral students. Best practices employed for recruitment and retention are built upon lessons learned from previous LSAMP BD host sites. The program will provide a robust set of graduate student opportunities that promote mentorship and leadership in STEM communities. These include workshops on such topics as writing technical reports and papers, learning the culture of the laboratory, building peer and professional relationships, planning for advancement to candidacy, successful grant writing, and presenting your work. Collaborations between UCI-LSAMP, the Graduate Division, and STEM departments will ensure the success of the BD Program. To date, the California LSAMP BD has supported 105 underrepresented students in STEM disciplines across all campuses of the University of California.", "AwardID" -> "1500284", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Irvine"], "Investigators" -> {Entity["NSFInvestigator", "HowardGillman"], Entity["NSFInvestigator", "DerekDunn-Rankin"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500284&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 10}, {"BD", 9}, {"LSAMP", 5}, {"students", 5}, {"graduate", 4}, {"Program", 4}, {"underrepresented", 4}, {"California", 3}, {"education", 3}, {"UCI", 3}, {"workforce", 3}, {"CAMP", 2}, {"cohort", 2}, {"competitive", 2}, {"completion", 2}, {"development", 2}, {"disciplines", 2}, {"diverse", 2}, {"diversity", 2}, {"doctoral", 2}, {"host", 2}, {"nation's", 2}, {"Native", 2}, {"NSF's", 2}, {"Ph.D.", 2}, {"practices", 2}, {"program", 2}, {"promote", 2}, {"recruitment", 2}, {"retention", 2}, {"student", 2}, {"support", 2}, {"University", 2}, {"writing", 2}}|>, "1500285" -> <|"AwardTitle" -> "Developing the multilayer multiconfiguration time-dependent Hartree theory", "AwardEffectiveDate" -> DateObject[{2014, 11, 1}], "AwardExpirationDate" -> DateObject[{2017, 6, 30}], "AwardAmount" -> Quantity[420000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03090000", "ProgramOfficer" -> "Evelyn M. Goldfield", "Abstract" -> "Haobin Wang, of New Mexico State University is supported by an award from the Chemical Theory, Models and Computational method in the Chemistry Division and the Computational and Data-Enabled Science and Engineering (CDS&E) program to develop and apply computational approaches to study electron transfer processes in several technologically-important materials and devices such as dye sensitized solar cells, molecular junction devices, and new electronic/magnetic materials. Because electrons are very small objects, they obey the laws of quantum mechanics. To get a sufficiently accurate description of many of these systems, quantum mechanical methods must be applied to both the electrons and the atomic nuclei. Professor Wang and his colleagues have developed an accurate and efficient quantum mechanical approach that is designed for this purpose called the multilayer-multiconfiguration time-dependent Hartree (ML-MCTDH) theory. The fundamental understanding resulting from this research contributes to the rational design of new materials such as for solar energy conversion and molecular electronics. The numerical techniques and software developed in this project have potential applications to a broad range of problems in science and engineering, e.g., numerical methods, signal compression, and parallel computation. Both undergraduate and graduate students contribute to this research. \n\nWith the extension of ML-MCTDH to the second quantization representation for treating identical particles, the theory is formally complete. The purpose of the current research is: (i) to investigate as many important physical models as possible that can be treated accurately via the current ML-MCTDH implementation; and (ii) to develop new algorithms within the ML-MCTDH framework to treat more general models. Specifically, the principal investigator and his coworkers apply the current theory to a variety of important and challenging problems in physics and chemistry, e.g., heterogeneous electron transfer using the Anderson-News model, spin relaxation where the electronic and nuclear spins are treated on equal footing, and the Kondo effect using the Anderson impurity model. Beyond those straightforward applications the current implementation of the ML-MCTDH theory is being extended to more general forms of potential energy functions. Further goals are to improve the relevant ML-MCTDH algorithms, e.g., using multilayer improved relaxation to generate the initial density matrix at low temperatures, grouping and streamlined evaluation of a series of operators, and modifying ML-MCTDH equations of motion that remove the regularization of the numerical singularities. The software developed in this research will be made freely available to the research community.", "AwardID" -> "1500285", "Institution" -> Entity["NSFInstitution", "UniversityOfColoradoAtDenver-DowntownCampus"], "Investigators" -> {Entity["NSFInvestigator", "HaobinWang"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Chemistry", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500285&HistoricalAwards=false"], "KeywordTally" -> {{"ML-MCTDH", 7}, {"research", 5}, {"current", 4}, {"theory", 4}, {"developed", 3}, {"e.g.", 3}, {"materials", 3}, {"new", 3}, {"numerical", 3}, {"quantum", 3}, {"using", 3}, {"accurate", 2}, {"algorithms", 2}, {"applications", 2}, {"apply", 2}, {"Computational", 2}, {"develop", 2}, {"devices", 2}, {"electron", 2}, {"electronic", 2}, {"electrons", 2}, {"energy", 2}, {"general", 2}, {"implementation", 2}, {"important", 2}, {"mechanical", 2}, {"methods", 2}, {"model", 2}, {"models", 2}, {"molecular", 2}, {"potential", 2}, {"problems", 2}, {"purpose", 2}, {"relaxation", 2}, {"software", 2}, {"solar", 2}, {"transfer", 2}, {"treated", 2}, {"Wang", 2}}|>, "1500286" -> <|"AwardTitle" -> "Operationalization of Visualization via Deconstruction", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2017, 8, 31}], "AwardAmount" -> Quantity[249868, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11040200", "ProgramOfficer" -> "Dawn Rickey", "Abstract" -> "Because chemistry explores phenomena that can be observed with the senses, but are explained based on the molecular-level behavior of invisible molecules, atoms, and ions, effective use of visual representations of molecular-level phenomena is essential for communicating about chemistry. Research also shows that there is a positive relationship between the ability to see chemical concepts among different representations and successful chemistry problem solving. Chemistry instructors may sometimes assume that, as their instruction addresses conceptual understanding, students' visualization skills will naturally develop. Consequently, instructors may not explicitly teach visualization skills and processes in their courses. This Improving Undergraduate STEM Education project will develop and test a set of ten modules to explicitly teach visualization skills and the use of visual representations to students in college chemistry courses. The modules will support students in understanding progressively more complex content and visual representations across the chemistry curriculum.\n\nEach of the ten modules will be developed, pilot tested, revised, and ultimately implemented in an upper-division chemistry course. In developing the modules, three main mechanisms will be employed to support students development of visualization skills: drawing attention to prominent features and patterns to reduce attention to extraneous information and cognitive load, decomposing a complex problem into more manageable parts, and problematizing to encourage students to make their ideas and thinking processes explicit. During the pilot-testing phase, the main data sources will include the copies of students' work on the activities and recorded sessions from focus groups. Analyses of these data will employ a drawing to learn framework to assess visualization objectives and an argumentation framework to assess problematization. In addition, the selection of representations included in the module activities will be evaluated for areas of visual attention using eye-tracking methodologies in conjunction with a retrospective think-aloud method. Once the modules have been pilot tested and revised, they will be implemented as a set during a one-semester intervention, scaffolding both chemistry content and visual complexity in representations. A rubric will be developed to track students' progress in the use of deconstruction as a problem solving strategy and sophistication in verbalization of visual mental constructs. Quantitative data from pre- and post-test scores on two standardized visualization tools will complement documentation of visualization gains, and the impact of the intervention on student achievement will be determined. Ultimately, the project will provide faculty with robust instructional materials that they can use in their classrooms to promote visualization and effective problem solving in chemistry.", "AwardID" -> "1500286", "Institution" -> Entity["NSFInstitution", "NorthCarolinaStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "MariaOliver-Hoyo"]}, "ProgramElements" -> {{"Code" -> "1536", "Text" -> "S-STEM:SCHLR SCI TECH ENG&MATH"}, {"Code" -> "1998", "Text" -> "IUSE"}}, "ProgramReferences" -> {{"Code" -> "8209", "Text" -> "Improv Undergrad STEM Ed(IUSE)"}, {"Code" -> "9178", "Text" -> "UNDERGRADUATE EDUCATION"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Undergraduate Education", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500286&HistoricalAwards=false"], "KeywordTally" -> {{"chemistry", 8}, {"visualization", 8}, {"students", 7}, {"representations", 6}, {"visual", 6}, {"modules", 5}, {"problem", 4}, {"skills", 4}, {"use", 4}, {"attention", 3}, {"data", 3}, {"solving", 3}, {"activities", 2}, {"assess", 2}, {"complex", 2}, {"content", 2}, {"courses", 2}, {"develop", 2}, {"developed", 2}, {"drawing", 2}, {"effective", 2}, {"explicitly", 2}, {"framework", 2}, {"implemented", 2}, {"instructors", 2}, {"intervention", 2}, {"main", 2}, {"molecular-level", 2}, {"phenomena", 2}, {"pilot", 2}, {"processes", 2}, {"project", 2}, {"revised", 2}, {"set", 2}, {"support", 2}, {"teach", 2}, {"ten", 2}, {"tested", 2}, {"understanding", 2}}|>, "1500292" -> <|"AwardTitle" -> "PFI:AIR - TT: Robust Multimaterial Chalcogenide Infrared Optical Fibers", "AwardEffectiveDate" -> DateObject[{2015, 4, 15}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating advances in the fabrication of multimaterial fibers to the production of mechanically stable optical fibers capable of transmitting light at mid-infrared (MIR) wavelengths for which limited commercially available optical-fiber options exist. The MIR range of the electromagnetic spectrum has recently become accessible (due to the development of semiconductor quantum cascade lasers) and this has opened up exciting applications in chemical sensing, environmental monitoring, and medical imaging. However, fully benefiting from these sensing, monitoring and imaging opportunities requires the development of optical fibers that cover the entire MIR spectrum, are affordable, robust, and easy to handle. This project addresses this critical need by leveraging recent NSF-funded fundamental discoveries in multimaterial fiber fabrication, where distinct materials are combined monolithically in a single fiber strand. The fiber's optical properties are dictated by an otherwise brittle MIR glass, while the superior mechanical properties stem from a robust built-in polymer jacket. The project will result in three distinct optical fiber prototypes packaged with standard end-connectors. When compared to the leading competing MIR fibers in this market space, the monolithic multimaterial optical fibers developed here will offer a broader optical spectral transmission window, lower cost, and superior mechanical robustness for ease of handling and manipulation.\n\nThis project, as it translates from research discovery toward commercial application, addresses the technology gap in robust optical fibers that have a transparency window covering the entire MIR spectrum and in which the dimension of the core and the index contrast between the core and cladding may be readily controlled. Recent breakthroughs are exploited in one-step multimaterial preform extrusion in which a fiber preform - a macroscopic scaled up model of the fiber - is extruded from a billet combining MIR chalcogenide glasses and a thermoplastic polymer. The preform is provided with a thick, built-in thermoplastic polymer jacket that is thermally compatible with the glass and thus they may be co-drawn into a fiber. Since the glass is sealed within the polymer, the preform is readily drawn continuously in an ambient environment into extended fiber lengths. The project will result in three fiber prototypes: a multimode fiber with a transmission window extending to a wavelength of 12 microns, a single-mode fiber for transmitting up to a wavelength of 6 microns, and high-refractive-index-contrast fiber tapers for nonlinear applications - particularly MIR supercontinuum generation. All three prototypes are endowed with superior mechanical properties and will be packaged with standard optical fiber connectors to be readily used in real-world settings. This project combines the efforts of a research scientist for fabrication and testing along with an MBA student for market analysis. The project co-PIs in turn combine technical and commercialization expertise and will leverage both the unique fiber fabrication facilities at the University of Central Florida along with business incubation and venture accelerator programs. \n\nIn addition, this technology translation effort will benefit from partnering with the IRFlex Corporation, The Mid-IR Fiber Devices Company, to assist with the transition from research discovery to commercial reality.", "AwardID" -> "1500292", "Institution" -> Entity["NSFInstitution", "UniversityOfCentralFlorida"], "Investigators" -> {Entity["NSFInvestigator", "AymanAbouraddy"], Entity["NSFInvestigator", "KennethSchepler"], Entity["NSFInvestigator", "GordonHogan"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500292&HistoricalAwards=false"], "KeywordTally" -> {{"fiber", 13}, {"MIR", 8}, {"optical", 8}, {"project", 7}, {"fibers", 6}, {"fabrication", 4}, {"multimaterial", 4}, {"polymer", 4}, {"preform", 4}, {"glass", 3}, {"mechanical", 3}, {"properties", 3}, {"prototypes", 3}, {"readily", 3}, {"research", 3}, {"robust", 3}, {"spectrum", 3}, {"superior", 3}, {"window", 3}, {"addresses", 2}, {"applications", 2}, {"built-", 2}, {"commercial", 2}, {"core", 2}, {"development", 2}, {"discovery", 2}, {"distinct", 2}, {"entire", 2}, {"imaging", 2}, {"jacket", 2}, {"market", 2}, {"microns", 2}, {"monitoring", 2}, {"packaged", 2}, {"result", 2}, {"sensing", 2}, {"standard", 2}, {"technology", 2}, {"thermoplastic", 2}, {"transmission", 2}, {"transmitting", 2}, {"wavelength", 2}}|>, "1500293" -> <|"AwardTitle" -> "PFI:AIR - TT: A Hybrid Metal/Glass Composite System for Multihazard Resilient Bridge Columns", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2017, 2, 28}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on translating a novel bridge column system to fill the need for cost-effective and sustainable bridges that are resilient to natural and man-made hazards such as earthquakes, terrorist attacks, vessel collisions/fires, and corrosive environments. The hybrid metal-glass composite column system is important because our nation is in critical need for durable and safe transportation infrastructure. Conventional structural materials, such as reinforced concrete and steel, are vulnerable to various hazards and environmental conditions. Traditional bridge construction methods are expensive, time consuming, and cause major traffic interruptions. This product enables accelerated construction of new bridges, increased work zone safety, and reduction of travel delays, which optimizes the stewardship of public funds to grow the nation?s infrastructure. The project will result in the proof-of-concept of a novel hybrid composite column system. This hybrid composite system integrates the unique energy dissipation of steel material, the excellent strength-to-weight ratio of glass fibers, and the exceptional durability of polymeric resins. These features provide the following advantages: superior structural performance, durability, cost-efficiency, and ease of construction when compared to the leading competing systems like conventional concrete-filled FRP tube (CFFT) systems in this market space. \n\nThis project addresses the following technology gaps as it translates from research discovery toward commercial application: 1) understanding morphology of hybrid steel-glass composites, 2) validating superior structural performance of the column system, 3) developing reliable structural design methodology, and 4) identifying and addressing potential scalability and manufacturing difficulties. A series of structural experiments will be performed on tubes with diverse composite architecture under various loading conditions. This will be complemented by high fidelity finite element simulations to optimize the design of the prototype. After finalizing the design, structural testing of a large-scale bridge column will be performed. In addition, personnel involved in this project including multiple graduate and undergraduate students, some from underrepresented groups, will receive entrepreneurship and technology translation experiences through collaboration with industry partners and communication with Departments of Transportation and bridge construction companies. \n\nThe project engages NOV Fiber Glass Systems to provide expertise in manufacturing of filament wound composite tubes and access to their testing facility in this technology translation effort from research discovery toward commercial reality.", "AwardID" -> "1500293", "Institution" -> Entity["NSFInstitution", "UniversityOfConnecticut"], "Investigators" -> {Entity["NSFInvestigator", "HadiBozorgmanesh"], Entity["NSFInvestigator", "KellyBurke"], Entity["NSFInvestigator", "ArashEsmailiZaghi"], Entity["NSFInvestigator", "MehdiSaiidi"]}, "ProgramElements" -> {{"Code" -> "7396", "Text" -> "NEES RESEARCH"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "036E", "Text" -> "CIVIL INFRASTRUCTURE"}, {"Code" -> "039E", "Text" -> "STRUCTURAL SYSTEMS"}, {"Code" -> "040E", "Text" -> "Haz mitigation of structural sys"}, {"Code" -> "043E", "Text" -> "EARTHQUAKE ENGINEERING"}, {"Code" -> "1057", "Text" -> "CIS BASE RESEARCH"}, {"Code" -> "1576", "Text" -> "NATIONL EARTHQK HZRD REDCT PRG"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "CVIS", "Text" -> "CIVIL INFRASTRUCTURE"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500293&HistoricalAwards=false"], "KeywordTally" -> {{"structural", 6}, {"column", 5}, {"composite", 5}, {"project", 5}, {"system", 5}, {"bridge", 4}, {"construction", 4}, {"hybrid", 4}, {"design", 3}, {"technology", 3}, {"br/>

", 2}, {"bridges", 2}, {"commercial", 2}, {"conditions", 2}, {"discovery", 2}, {"durability", 2}, {"following", 2}, {"hazards", 2}, {"infrastructure", 2}, {"manufacturing", 2}, {"nation", 2}, {"need", 2}, {"novel", 2}, {"performance", 2}, {"performed", 2}, {"provide", 2}, {"research", 2}, {"steel", 2}, {"superior", 2}, {"systems", 2}, {"testing", 2}, {"translation", 2}, {"tubes", 2}, {"various", 2}}|>, "1500297" -> <|"AwardTitle" -> "Conferences in Formal Power Series and Algebraic Combinatorics, 2015 and 2016", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2017, 4, 30}], "AwardAmount" -> Quantity[54896, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This award will provide support for US participants, especially women, graduate students, postdocs, and junior faculty, to attend the twenty-seventh and twenty-eighth international conferences in Formal Power Series and Algebraic Combinatorics (FPSAC). The 2015 edition will be held in Daejeon, South Korea, on July 6-10, 2015 (more info on the website http://fpsac.combinatorics.kr/). The 2016 edition will be held in Vancouver, Canada, on July 4-8, 2016 (more info on the website https://sites.google.com/site/fpsac2016/).\n\nThe most important annual conference series in algebraic combinatorics in the world, FPSAC offers young American researchers a unique opportunity to interact closely with top mathematicians from many countries. Somewhat interdisciplinary, the conferences link research in combinatorics to other topics in pure mathematics such as algebraic geometry, commutative algebra, representation theory, K-theory and symplectic geometry, and to topics in other sciences such as computer science, physics, and biology. Each conference, which includes nine one-hour plenary lectures, thirty half-hour contributed talks, and forty posters, will attract over 200 participants from all over the world.", "AwardID" -> "1500297", "Institution" -> Entity["NSFInstitution", "DartmouthCollege"], "Investigators" -> {Entity["NSFInvestigator", "SergiElizalde"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500297&HistoricalAwards=false"], "KeywordTally" -> {{"2015", 2}, {"2016", 2}, {"algebraic", 2}, {"combinatorics", 2}, {"conference", 2}, {"conferences", 2}, {"edition", 2}, {"FPSAC", 2}, {"geometry", 2}, {"held", 2}, {"info", 2}, {"July", 2}, {"participants", 2}, {"topics", 2}, {"website", 2}, {"world", 2}}|>, "1500302" -> <|"AwardTitle" -> "Conference on Complex Analysis and Geometry", "AwardEffectiveDate" -> DateObject[{2015, 1, 1}], "AwardExpirationDate" -> DateObject[{2015, 12, 31}], "AwardAmount" -> Quantity[23335, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "This award provides funding support to the Conference on Complex Analysis and Geometry to be held on the campus of the University of Wisconsin-Madison on March 27-29, 2015. The conference is devoted to recent developments in several complex variables in connections with fields of harmonic analysis, partial differential equations, conformal geometry, complex geometry, and dynamical systems. It will feature 10 main speakers who are leading mathematicians or junior researchers who have made significant contributions to the fields. There will also be 5 short-talks presented by young researchers who obtained their Ph.D. recently. The conference will create opportunity for exchange of new research results and new frontiers, which will benefit the recent Ph.D.'s and graduate students. The organizers encourage women and members of underrepresented minority groups to participate in the conference, and partial travel support will be provided. \n\nThe conference will feature recent research results and methods in several complex variables. The main topics of the conference include the normal form theory in several complex variables and dynamical systems, extension property of biholomorphic mappings, d-bar-Neumann problems, the rigidity and classification of holomorphic mappings between balls, the local and global theory of CR manifolds, Levi-flat hypersurfaces and the lamination theory in complex projective spaces.", "AwardID" -> "1500302", "Institution" -> Entity["NSFInstitution", "UniversityOfWisconsin-Madison"], "Investigators" -> {Entity["NSFInvestigator", "XianghongGong"], Entity["NSFInvestigator", "BrianStreet"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500302&HistoricalAwards=false"], "KeywordTally" -> {{"complex", 5}, {"conference", 5}, {"recent", 3}, {"theory", 3}, {"variables", 3}, {"dynamical", 2}, {"feature", 2}, {"fields", 2}, {"geometry", 2}, {"main", 2}, {"mappings", 2}, {"new", 2}, {"partial", 2}, {"research", 2}, {"researchers", 2}, {"results", 2}, {"support", 2}, {"systems", 2}}|>, "1500306" -> <|"AwardTitle" -> "EAGER: Collaborative Research: Conceptualizing sustained environmental information management in the landscape of current and emerging eco-informatics infrastructure", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[139682, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08080000", "ProgramOfficer" -> "Peter H. McCartney", "Abstract" -> "The data generated by environmental research are highly valuable, not only because of the cost of research but also because they are irreplaceable and needed for understanding change. A major challenge for all research entities is the management of this digital asset and associated information for maintaining its value. This challenge is complex in nature, covering not only the collection and storage of data, but also the creation of relevant (and sufficient) information about the data (metadata), such that they can be re-used broadly. Several environmental data repositories and data management approaches have been developed over the past few years. It is now time to seek input from researchers in the role of data authors and data re-users and data managers, to expansively explore the current operating environment, potential collaboration opportunities, efficiencies of scale, and future community needs for this challenge to be addressed effectively. An initial workshop will allow these stakeholders to share their expertise, experience and future requirements with their colleagues. The output from this initial exercise will then feed into a second session, which will result in strategic recommendations detailing the activities needed to create a collaborative and efficient data management infrastructure capable of supporting future environmental science research endeavors. \n\nMost current environmental data repositories fulfill specific needs or objectives, i.e., archiving and disseminating data from a project, network of research sites, institution, a specific funding source, or to accompany paper publications. Envisioning a sustained Scientific Data Infrastructure (SDI), and with the goal of providing high quality data to researchers, policy makers and the general public, this project concentrates on data repositories and current curation practices as an integral part of this vision. Within this scope and in the context of environmental research data management, original goals and objectives of single repositories will be re-evaluated, efficiencies of scale identified, a cost-benefit analyses for some centralized services attempted, and new, sustainable collaborations conceptualized. Specifically, data curators from a range of environmental research fields, data aggregators, tool developers, computer scientists and environmental scientists (both data providers and users) will be brought together for an informed dialog which draws on this broad collective experience. A preliminary information-gathering phase will describe the characteristics of each repository to inform the discussion at two subsequent community workshops. The first workshop will identify new collaboration and curation strategies that also cater to the currently underserved single investigators and move environmental data from \"available\" to \"usable\", in order to accelerate scientific inquiry. The second workshop will examine these strategies further, and develop one or more alternative, community-vetted roadmaps for research information management with the goal of more efficiently and sustainably utilizing NSF investments. In summary, these workshops will produce a strategic implementation plan outlining one or more options for a sustained environmental data management infrastructure capable of accelerating scientific inquiry, serve all contributing investigators (data producers) and provide the basis for education and outreach activities in a cost effective approach. Data management needs are fairly well understood. Organizational, personnel and management structures are not. Hence, the plan will focus on these challenges while also considering workforce development. A website for this project will be established at http://sedicollaborative.org.", "AwardID" -> "1500306", "Institution" -> Entity["NSFInstitution", "UniversityOfWisconsin-Madison"], "Investigators" -> {Entity["NSFInvestigator", "CorinnaGries"]}, "ProgramElements" -> {{"Code" -> "1165", "Text" -> "ADVANCES IN BIO INFORMATICS"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Div Of Biological Infrastructure", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500306&HistoricalAwards=false"], "KeywordTally" -> {{"data", 20}, {"environmental", 9}, {"management", 8}, {"research", 8}, {"repositories", 4}, {"challenge", 3}, {"current", 3}, {"future", 3}, {"information", 3}, {"needs", 3}, {"project", 3}, {"workshop", 3}, {"activities", 2}, {"capable", 2}, {"collaboration", 2}, {"community", 2}, {"cost", 2}, {"curation", 2}, {"Data", 2}, {"efficiencies", 2}, {"experience", 2}, {"goal", 2}, {"infrastructure", 2}, {"initial", 2}, {"inquiry", 2}, {"investigators", 2}, {"needed", 2}, {"new", 2}, {"objectives", 2}, {"plan", 2}, {"researchers", 2}, {"scale", 2}, {"scientific", 2}, {"scientists", 2}, {"second", 2}, {"single", 2}, {"specific", 2}, {"strategic", 2}, {"strategies", 2}, {"sustained", 2}, {"workshops", 2}}|>, "1500309" -> <|"AwardTitle" -> "Collaborative Research: Understanding and Reducing Student Resistance as a Barrier to Faculty Change", "AwardEffectiveDate" -> DateObject[{2014, 8, 10}], "AwardExpirationDate" -> DateObject[{2016, 8, 31}], "AwardAmount" -> Quantity[163609, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11040000", "ProgramOfficer" -> "Dawn Rickey", "Abstract" -> "This WIDER research project focuses on understanding student resistance as a barrier to STEM faculty adoption of evidence-based teaching methods in the context of introductory engineering courses at University of Michigan, Virginia Tech, North Carolina A & T, and Bucknell University. The project is investigating three related research questions, including: 1) What factors (including faculty strategies, student experience, institution and course type, and student and faculty characteristics) influence student resistance to nontraditional teaching methods? 2) To what extent does expectancy violation theory explain student resistance to nontraditional teaching methods? and 3) What specific, evidence-based strategies (and in what contexts) can faculty employ to significantly reduce student resistance? To address these questions, the project team is employing rigorous instrument development procedures to design surveys to measure student resistance and expectancy violation, and conducting in-depth studies at a range of institutions, combining qualitative methods with quantitative surveys to identify additional factors related to student resistance. The final phase of the project includes a full-scale study of 20 introductory engineering courses. Expected products include evidence-based strategies faculty can use to reduce student resistance, student surveys that faculty can use to monitor their own progress in reducing student resistance, and a classroom observation protocol focusing on student resistance.", "AwardID" -> "1500309", "Institution" -> Entity["NSFInstitution", "UniversityOfTexasAtAustin"], "Investigators" -> {Entity["NSFInvestigator", "MauraBorrego"]}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Undergraduate Education", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500309&HistoricalAwards=false"], "KeywordTally" -> {{"student", 12}, {"resistance", 9}, {"faculty", 6}, {"methods", 4}, {"project", 4}, {"evidence-based", 3}, {"strategies", 3}, {"surveys", 3}, {"teaching", 3}, {"courses", 2}, {"engineering", 2}, {"expectancy", 2}, {"factors", 2}, {"including", 2}, {"introductory", 2}, {"nontraditional", 2}, {"questions", 2}, {"reduce", 2}, {"related", 2}, {"research", 2}, {"University", 2}, {"use", 2}, {"violation", 2}}|>, "1500310" -> <|"AwardTitle" -> "Women Achieving Tenure-Track Success: Strategies to Enable Community-based Retention", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2020, 2, 29}], "AwardAmount" -> Quantity[749779, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "dana britton", "Abstract" -> "The University of Washington, North Carolina State University, and California Polytechnic State Institute, San Luis Obispo submitted an ADVANCE PLAN D project whose overall goal is to increase the retention and advancement of women in academic careers to create greater diversity in engineering leadership. This project will build and facilitate a community-centric mentoring, networking, and career development program and will target early career women in electrical engineering and underrepresented minority women in engineering and computer science. The early career women (postdoctoral and early-career faculty stage) will be supported through cross-career stage networking, community building, career development symposia, and peer Mentoring Circles. \n\nThe project adapts two previously successful efforts at the University of Washington: 1) Women Evolving the Biological Sciences (WEBS): professional development symposia for early-career women in ecology and evolution and 2) Broadening the Representation of Academic Investigators in NeuroScience (BRAINS): symposia followed by Mentoring Circles for early career underrepresented minority neuroscientists. This project will examine how best to adapt these successful programs to two new disciplines and develop a model framework to allow others to develop such programs for a wide variety of fields and populations. To maximize program impact, the team will use ethnographic research methods to study the process and unique features of program development such as the collaboration between engineers and social scientists to develop new knowledge on the principles and processes critical to planning, implementing, and adapting successful intervention programs. The evaluation of the project will identify best practices to support women's success in academic careers and to diversify the engineering professoriate. The guiding principles and values that enable these programs to have impact on participants will be identified and codified in a framework that will be shared through the University of Washington's ADVANCE online \"LEAD-it-Yourself!\" toolkit.\n\nThe NSF ADVANCE Partnerships for Learning and Adaptation Networks (PLAN) program track supports projects that promote the adaptation and implementation of previously effective ADVANCE programs in new contexts and the testing of innovative strategies to promote the participation, success, and advancement of women in STEM academic careers. PLAN projects also contribute to the knowledge base on gender equity in STEM academic careers. The PLAN-D funding track is designed to expand the application of proven-successful gender-equity initiatives for STEM faculty in a specific disciplinary area through networked adaptation of a specific program or initiative. Careful evaluation is expected to expand understanding of such initiatives in a disciplinary context.", "AwardID" -> "1500310", "Institution" -> Entity["NSFInstitution", "UniversityOfWashington"], "Investigators" -> {Entity["NSFInvestigator", "EveRiskin"], Entity["NSFInvestigator", "JoyceYen"], Entity["NSFInvestigator", "ClaireHorner-Devine"]}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500310&HistoricalAwards=false"], "KeywordTally" -> {{"women", 6}, {"career", 5}, {"program", 5}, {"programs", 5}, {"project", 5}, {"academic", 4}, {"ADVANCE", 4}, {"careers", 4}, {"development", 4}, {"engineering", 4}, {"University", 4}, {"develop", 3}, {"early", 3}, {"new", 3}, {"PLAN", 3}, {"STEM", 3}, {"successful", 3}, {"symposia", 3}, {"adaptation", 2}, {"advancement", 2}, {"best", 2}, {"Circles", 2}, {"disciplinary", 2}, {"early-career", 2}, {"evaluation", 2}, {"expand", 2}, {"faculty", 2}, {"framework", 2}, {"impact", 2}, {"initiatives", 2}, {"knowledge", 2}, {"Mentoring", 2}, {"minority", 2}, {"networking", 2}, {"previously", 2}, {"principles", 2}, {"projects", 2}, {"promote", 2}, {"specific", 2}, {"stage", 2}, {"State", 2}, {"success", 2}, {"track", 2}, {"underrepresented", 2}, {"Washington", 2}}|>, "1500314" -> <|"AwardTitle" -> "PFI:AIR - TT: Highly Sensitive Eye-safe Flash LiDARs based on Nanoinjection Detectors", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 9, 30}], "AwardAmount" -> Quantity[199071, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07070000", "ProgramOfficer" -> "Barbara H. Kenny", "Abstract" -> "This PFI: AIR Technology Translation project focuses on improving the 3-dimensional (3D) imaging of structures. 3D imaging has applications in environmental mapping, ecological characterization, robots and automation, medical imaging, areal mapping, and defense. This project will use electron injection detectors developed at Northwestern to develop a 3D imaging technique that can be accomplished without moving parts, using laser illuminated detection and ranging (LIDAR) large detector arrays (\"flash LIDAR\"). Most current LIDAR systems use a small number of avalanche detectors and mechanical scanning methods to produce an image. Electron injection detectors, as proposed here, offer a promising alternative to avalanche detectors because they require less voltage and use less power, and can be made into large two-dimensional arrays. If successful, the proposed work could lead to \"staring\" LIDAR systems, which do not need mechanical scanning and produce a high-resolution 3D image in one shot. The system would be smaller, lighter and lower cost than existing 3D imaging systems with mechanical scanning. These improvements could enable 3D imagers to become as ubiquitous as digital cameras are today. \n\nThis project addresses the following technology gap as it translates from research discovery toward commercial application: increasing the speed of electron injection detectors to enhance the ranging resolution. While the current devices are fast, they do not demonstrate gigahertz (GHz) speed. One of the limitations in achieving this speed is the parasitic capacitances, which will be addressed as part of the research effort. Also, high-bandwidth trans-impedance amplifiers will be used, an improvement over current existing voltage amplifiers. In addition to the PI, co-PI, and the personnel from sub-contracting company, there will be one graduate student who will receive significant technical training. The student will also learn directly from the commercialization work planned for the project, and from entrepreneurship courses offered by the McCormick School of Engineering. \n\nThe project engages Michigan Aerospace, which has significant expertise in LIDAR system, to help identify the best tradeoff between different design parameter in this technology translation effort from research discovery toward commercial reality.", "AwardID" -> "1500314", "Institution" -> Entity["NSFInstitution", "NorthwesternUniversity"], "Investigators" -> {Entity["NSFInvestigator", "HoomanMohseni"], Entity["NSFInvestigator", "NathanielHarrison"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Industrial Innovation & Partnersh", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500314&HistoricalAwards=false"], "KeywordTally" -> {{"3D", 6}, {"detectors", 5}, {"imaging", 5}, {"LIDAR", 5}, {"project", 5}, {"current", 3}, {"injection", 3}, {"mechanical", 3}, {"research", 3}, {"scanning", 3}, {"speed", 3}, {"systems", 3}, {"use", 3}, {"amplifiers", 2}, {"arrays", 2}, {"avalanche", 2}, {"br/>

", 2}, {"commercial", 2}, {"discovery", 2}, {"effort", 2}, {"electron", 2}, {"existing", 2}, {"image", 2}, {"large", 2}, {"mapping", 2}, {"produce", 2}, {"proposed", 2}, {"ranging", 2}, {"significant", 2}, {"student", 2}, {"system", 2}, {"technology", 2}, {"voltage", 2}, {"work", 2}}|>, "1500316" -> <|"AwardTitle" -> "Selmer Groups, Euler Systems, and Rational Points on Curves", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[169999, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "This project concerns work in the general area of number theory, which is studied in this proposal using methods from geometry. Algebraic varieties -- geometric objects defined by equations -- play a central role in many parts of mathematics, including its most applied areas. For example, special algebraic varieties called elliptic curves are used in algorithms to encrypt data for transmission and for efficient digital signatures. In its most basic form, an elliptic curve is a curve defined by a certain type of polynomial equation in two variables. Historically number theorists have been interested in finding solutions of these equations in which the variables take values that are either whole numbers or fractions. The investigator will study some new questions about points on algebraic varieties, and the connections between these points and other mathematical objects and concepts.\n\nSome of the most basic and important questions in number theory are about rational points on varieties. These questions include connections with L-functions, such as the Birch and Swinnerton-Dyer conjecture. In this project the investigator plans to use many different techniques, including algebraic, p-adic, and analytic tools, to study various aspects of these questions. One set of questions to be studied includes refined class number formulas over number fields and higher rank Kolyvagin systems. In previous work of the investigator, Kolyvagin systems have proved to be a very useful tool for relating L-values and arithmetic. In another direction, the investigator plans to use Selmer groups of twists of abelian varieties to study how the set of rational points on a curve changes when the base field is increased.", "AwardID" -> "1500316", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Irvine"], "Investigators" -> {Entity["NSFInvestigator", "KarlRubin"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500316&HistoricalAwards=false"], "KeywordTally" -> {{"number", 5}, {"questions", 5}, {"varieties", 5}, {"investigator", 4}, {"points", 4}, {"algebraic", 3}, {"curve", 3}, {"study", 3}, {"basic", 2}, {"connections", 2}, {"defined", 2}, {"elliptic", 2}, {"equations", 2}, {"including", 2}, {"Kolyvagin", 2}, {"objects", 2}, {"plans", 2}, {"project", 2}, {"rational", 2}, {"set", 2}, {"studied", 2}, {"systems", 2}, {"theory", 2}, {"use", 2}, {"variables", 2}, {"work", 2}}|>, "1500317" -> <|"AwardTitle" -> "Cohort 12: JSU Bridge to the Doctorate", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Dr. A. James Hicks", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the Science, Technology, Engineering, and Mathematics (STEM) workforce through the development of highly competitive students from groups historically underrepresented in STEM disciplines: African-Americans, Alaska Natives, American Indians, Hispanic Americans, Native Hawaiians, and Native Pacific Islanders. The goal of the LSAMP Bridge to the Doctorate (BD) Activity is to increase the quantity and quality of STEM graduate students from underrepresented populations, with emphasis on Ph.D. matriculation and completion. In order to maintain the United States of America's global leadership in STEM, it needs to develop the untapped pool of creative and talented students historically underrepresented, who earn Ph.Ds in STEM . Jackson State University (JSU), a Historically Black University (HBCU) and lead institution for the Mississippi LSAMP (LSMAMP), will serve as the host site for the 2015-2017 cohort of BD Fellows. JSU will execute a BD program that is based upon challenging research and academic experiences. This program contributes to addressing one of the objectives in NSF's 2014-2018 Strategic Plan, namely to \"integrate education and research to support development of a diverse STEM workforce with cutting-edge capabilities.\" JSU's BD Program will contribute significantly to increasing the diversity of scientists, mathematicians and engineers in academia and the STEM workforce, thereby helping the nation to remain globally competitive.\n\nJackson State University's Bridges to the Doctorate Program has four objectives, which are focused on (i) research and academic preparation, (ii) enrichment activities, (iii) national and international partnerships, and (iv) evaluation and student tracking. JSU has a strong track record for preparing primarily African American graduate students in biology, chemistry, mathematics, environmental science, computer science, and engineering doctoral degrees. To date, 97 out of the 117 BD Fellows from previous cohorts have been admitted into STEM doctoral programs; 27 out of the 97 have earned their Ph.D.s and 54 are progressing well towards earning their doctorate. JSU's two-pronged approach of rigorous research training and compassionate and committed mentoring will enable their BD program to continue to prepare and increase the quality and quantity of students historically underrepresented in STEM entering the Ph.D. pathway.", "AwardID" -> "1500317", "Institution" -> Entity["NSFInstitution", "JacksonStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "AshtonHamme"], Entity["NSFInvestigator", "CarolynMeyers"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500317&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 9}, {"BD", 6}, {"students", 5}, {"program", 4}, {"research", 4}, {"underrepresented", 4}, {"historically", 3}, {"JSU", 3}, {"LSAMP", 3}, {"workforce", 3}, {"97", 2}, {"academic", 2}, {"American", 2}, {"development", 2}, {"doctoral", 2}, {"Doctorate", 2}, {"Fellows", 2}, {"graduate", 2}, {"increase", 2}, {"JSU's", 2}, {"Native", 2}, {"objectives", 2}, {"Ph.D.", 2}, {"Program", 2}, {"quality", 2}, {"quantity", 2}, {"science", 2}, {"State", 2}, {"University", 2}}|>, "1500320" -> <|"AwardTitle" -> "2015-2017 LSAMP Bridge to the Doctorate: Tennessee LSAMP Bridge to the Doctorate Program at Vanderbilt University", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Dr. A. James Hicks", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the STEM workforce through their efforts at significantly increasing the numbers of students from historically underrepresented minority populations to successfully complete high quality degree programs in science, technology, engineering and mathematics (STEM) disciplines. The LSAMP Bridge to the Doctorate (LSAMP-BD) activity provides two-year support at the post baccalaureate level for students from historically underrepresented minority populations to matriculate in STEM graduate programs with the ultimate goal of earning a doctoral degree in a STEM discipline. Participants are selected from LSAMP institutions nationwide. The Tennessee Louis Stokes Alliance for Minority Participation (TLSAMP), under the leadership of Tennessee State University, has chosen Vanderbilt University as the first LSAMP Bridge to the Doctorate (LSAMP-BD) site managed by this alliance. Vanderbilt University will host the 2015-2017 BD program in which a cohort of twelve LSAMP BD students will engage in STEM research, academics and professional development leading to acceptance and completion of the doctoral program. The Tennessee LSAMP graduate BD program at Vanderbilt University has the potential to promote systemic change in graduate education practices and policy, in ways that will increase the success of individual students on the doctoral pathway and the effectiveness of STEM graduate programs with a goal of diversifying America's STEM workforce. \n\nThe BD program at Vanderbilt University employs a proven \"toolkit\" with components for innovative recruitment, engagement, retention, student tracking and dissemination that will include a mentoring e-dashboard to advance the practice of mentoring formatively and real-time for tracking student progress and development. The toolkit also accommodates interview protocols and non-cognitive skills rubrics that has the potential to transform traditional graduate education practices. The program includes collaborations and linkages with other STEM networks and resources as well as other graduate programs, such as NSF's Graduate Research Fellowship Program (GRFP), Alliances for Graduate Education and the Professoriate (AGEP), Centers of Research Excellence in Science and Technology (CREST) and institutional resources to ensure students successful completion of the STEM doctoral degree. The program will be externally evaluated and students will be tracked throughout the program and into STEM careers following completion of STEM doctoral degree programs.", "AwardID" -> "1500320", "Institution" -> Entity["NSFInstitution", "TennesseeStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "KnowlesOverholser"], Entity["NSFInvestigator", "LonnieSharpe"], Entity["NSFInvestigator", "KeivanStassun"], Entity["NSFInvestigator", "MarkHardy"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500320&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 11}, {"program", 8}, {"graduate", 6}, {"LSAMP", 6}, {"students", 6}, {"doctoral", 5}, {"programs", 5}, {"University", 5}, {"BD", 4}, {"degree", 4}, {"Vanderbilt", 4}, {"completion", 3}, {"Tennessee", 3}, {"Alliances", 2}, {"Bridge", 2}, {"development", 2}, {"diversifying", 2}, {"Doctorate", 2}, {"education", 2}, {"goal", 2}, {"Graduate", 2}, {"historically", 2}, {"Louis", 2}, {"LSAMP-BD", 2}, {"mentoring", 2}, {"minority", 2}, {"Minority", 2}, {"Participation", 2}, {"populations", 2}, {"potential", 2}, {"practices", 2}, {"Research", 2}, {"resources", 2}, {"Stokes", 2}, {"student", 2}, {"toolkit", 2}, {"tracking", 2}, {"underrepresented", 2}, {"workforce", 2}}|>, "1500334" -> <|"AwardTitle" -> "Moduli Spaces in Algebraic Geometry", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[252001, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "Algebraic geometry provides a powerful theory with which to define moduli spaces (spaces of solutions of geometric problems) for interesting mathematical objects. Once they are defined, there are natural compelling questions about their geometry and topology. What do they look like? Are they irreducible, connected, of what dimension? Are they smooth? if not, what singularities arise? What structure is exhibited by their cohomology rings, and why should it be geometrically expected? What are their equations? The investigator intends to address many of these fundamental problems in a number of cases. The investigator has a track record of sustained and serious effort both in outreach to students at all levels (high school, undergraduate, and graduate), and in building institutions in which algebraic geometry can grow. The investigator will continue to attract graduate students into algebraic geometry and continue to nurture the careers of graduate students, post-docs, and young researchers. The investigator will also continue to work with large numbers of students at the secondary and undergraduate levels, attracting students into the mathematical sciences.\n\nThe investigator works in algebraic geometry, although his interests connect to other areas of mathematics, including topology, combinatorics, physics (string theory), number theory, and symplectic and differential geometry. This proposal, continuing various strands of the investigator's work, deals with moduli spaces and related notions in a variety of settings. In particular, the proposal deals with a number of fundamental questions regarding the foundations of \"tropical\" geometry, the stabilization of moduli spaces in the Grothendieck ring, the study of K3 surfaces through elliptic fibrations, and the topology of various moduli spaces of curves.", "AwardID" -> "1500334", "Institution" -> Entity["NSFInstitution", "StanfordUniversity"], "Investigators" -> {Entity["NSFInvestigator", "RaviVakil"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500334&HistoricalAwards=false"], "KeywordTally" -> {{"geometry", 7}, {"investigator", 5}, {"spaces", 5}, {"students", 5}, {"moduli", 4}, {"algebraic", 3}, {"continue", 3}, {"graduate", 3}, {"number", 3}, {"theory", 3}, {"topology", 3}, {"deals", 2}, {"fundamental", 2}, {"levels", 2}, {"mathematical", 2}, {"problems", 2}, {"proposal", 2}, {"questions", 2}, {"undergraduate", 2}, {"various", 2}, {"work", 2}}|>, "1500343" -> <|"AwardTitle" -> "Connectivity and Structure in Representable Matroids", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[129786, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "When communicating a digital message, errors can occur in the transmission for a variety of reasons. To ensure the original message is received by the recipient, some overhead is added, resulting in a so-called error-correcting code. There is always a trade-off between the number of errors that can be corrected and the amount of overhead that gets added to the message. This project is concerned with the study of mathematical abstractions of these error-correcting codes. Through these abstractions, called matroids, More will be learned about the optimal tradeoff between error-correcting capacity and overhead. Part of the investigations will use the open-source software SageMath, and it is expected that improvements to that software will be contributed. Graduate student involvement in the research is anticipated. \n\nNot only error-correcting codes, but also constraints in an optimization problem, path systems in a graph, and many other mathematical structures can be modeled by geometric configurations of points, known as matroids. Matroid theory gives a unique perspective on these structures through the introduction of concepts like connectivity and minors, both of which generalize concepts from graph theory. A matroid representation is a collection of vectors capturing the same geometric information as the abstract matroid. Geelen, Gerards, and Whittle have developed a powerful theory regarding the structure of matroids representable over a finite field. The first goal of this project is to study consequences of their result in coding theory, extremal matroid theory, and matroid flow problems. The second goal is to give a characterization of the class of dyadic matroids in terms of minimal obstructions known as excluded minors. Dyadic matroids are representable over both the field with 3 and with 5 elements, and arise, for instance, in the study of bidirected networks. The third goal is to study alternative representations, in particular multilinear and skew-partial field representations, which are useful in the theory of secret sharing, and connectivity related matroids, which arise naturally from the study of matroid structure. Computational science is increasingly used in matroid theory research. Especially the second line of research outlined above will benefit from versatile, reliable software for matroid computation. Recently Pendavingh and Van Zwam developed such software, which is part of the open-source, freely available SageMath software system. A final goal of the project is to improve on this functionality.", "AwardID" -> "1500343", "Institution" -> Entity["NSFInstitution", "LouisianaStateUniversity&AgriculturalAndMechanicalCollege"], "Investigators" -> {Entity["NSFInvestigator", "StefanHVanZwam"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500343&HistoricalAwards=false"], "KeywordTally" -> {{"matroid", 7}, {"theory", 7}, {"matroids", 6}, {"software", 5}, {"study", 5}, {"error-correcting", 4}, {"goal", 4}, {"field", 3}, {"message", 3}, {"overhead", 3}, {"project", 3}, {"research", 3}, {"abstractions", 2}, {"added", 2}, {"arise", 2}, {"codes", 2}, {"concepts", 2}, {"connectivity", 2}, {"developed", 2}, {"errors", 2}, {"geometric", 2}, {"graph", 2}, {"known", 2}, {"mathematical", 2}, {"minors", 2}, {"open-source", 2}, {"representable", 2}, {"representations", 2}, {"SageMath", 2}, {"second", 2}, {"structure", 2}, {"structures", 2}}|>, "1500361" -> <|"AwardTitle" -> "Workshop on Analysis and Geometry in Several Complex Variables", "AwardEffectiveDate" -> DateObject[{2014, 12, 1}], "AwardExpirationDate" -> DateObject[{2015, 11, 30}], "AwardAmount" -> Quantity[48400, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "A workshop titled \"Analysis and Geometry in Several Complex Variables\" will be held at Texas A&M University Qatar in Doha, Qatar, January 4-8, 2015. This workshop will bring together leading researchers, young post-docs, and graduate students from the Gulf region, Brazil, the US, and Europe. A website has been set up for this workshop at http://science.qatar.tamu.edu/Conferences/Pages/Upcoming-Conferences.aspx. The purpose of the workshop is twofold. First, to generate long term collaborations between mathematicians from the different regions. Second, to afford the younger participants an opportunity to interact with leaders in their field, as well as with each other. The subject matter, several complex variables, enjoys a central position in mathematics because it draws from, and contributes to, various other subareas of mathematics. But while it is amply motivated within mathematics proper, it also arises in various other contexts. For example, causality, one of the fundamental laws of nature, when transcribed via a mathematical device called Fourier transform, immediately leads to analytic functions of several (in this case four) complex variables.\n\nWhile the Sobolev theory of the Cauchy-Riemann equation(s) is well developed, the theory for the analogue on CR submanifolds, the tangential Cauchy-Riemann equation(s), is at a comparable stage only for submanifolds of hypersurface type. But even in these cases, fundamental questions concerning compactness, global regularity, etc., remain open. It has become clear that in order to address these questions, and to extend the theory to CR submanifolds that are not of hypersurface type, techniques of modern CR geometry will be crucial. CR functions and CR mappings arise naturally form the tangential Cauchy-Riemann operator, as functions in the kernel and as mappings that respect the CR structures (the basic object), respectively. A number of classical questions remain open in this very active area of research as well. By bringing together experts from these areas, the proposed workshop aims to initiate collaborations that will lead to substantial progress on these issues. \nIn addition, a short course on complex Brunn-Minkowski theory will provide an introduction to an exciting new perspective on some of the \"classical\" techniques.", "AwardID" -> "1500361", "Institution" -> Entity["NSFInstitution", "TexasA&MUniversityMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "EmilStraube"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500361&HistoricalAwards=false"], "KeywordTally" -> {{"CR", 6}, {"workshop", 5}, {"theory", 4}, {"Cauchy-Riemann", 3}, {"complex", 3}, {"functions", 3}, {"mathematics", 3}, {"questions", 3}, {"submanifolds", 3}, {"classical", 2}, {"collaborations", 2}, {"equation", 2}, {"fundamental", 2}, {"hypersurface", 2}, {"mappings", 2}, {"open", 2}, {"Qatar", 2}, {"remain", 2}, {"s", 2}, {"tangential", 2}, {"techniques", 2}, {"type", 2}, {"various", 2}}|>, "1500363" -> <|"AwardTitle" -> "Collaborative Research: Plasma Physics At Small Coulomb Logarithms", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[15000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "This collaborative research project will advance fundamental understanding of how groups of high speed ions crash into and interact with each other. One can measure just how violent a collision is by comparing the energy of the crashing high-speed ions with the electrical force between them. The most violent ion collisions, the ones that are most important both for extending our scientific knowledge and for developing technological applications, are very difficult to measure or calculate. They occur in extremely hot and very dense gases of charged particles called plasmas. In this project, new ideas will be used to measure and understand these collisions. Lasers will be used to slow atoms from speeds of nearly 1000 meters per second to a crawl of about an inch per second; and then to turn these slow atoms into ions. Additional lasers will then be used to measure how these ions crash into each other. The ions in these slow-motion collisions have the same amount of crash energy compared to the ion-ion electrical force, which means that the collision results can be directly compared to similar collisions at any energy. This project will use state-of-the-art large-scale computer simulations to make movies of the ion-ion collisions and compare these to the experimental measurements. When the computations are proven to be sufficiently accurate, approximations will be gradually introduced and tested in order to speed up the computations. These results will then set the standard for accurate and fast computations of ion collisions in plasmas. Several students will work on this project: Undergraduate and graduate students and post-doctoral scientists will work closely with expert scientists at Willamette University (Oregon), Brigham Young University (Utah), and the New Mexico Consortium (New Mexico).\n\nThe proposed collaborative research project will investigate energy relaxation in a system in which the value of the Coulomb logarithm is small. This is typical of high-energy-density systems, where violent small-impact-parameter collisions result in large particle deflections. Understanding these collisions is a priority for advancing fundamental plasma physics and for accurately modeling small impact parameter collisions in high energy density plasmas. The proposed work will generate high quality data in plasma regimes where traditional diagnostics are limited. The proposed work will combine data from a new dual-species ultracold neutral plasma experiment and state-of-the-art simulations to study temperature equilibration in moderately coupled plasmas, in which classic plasma assumptions are invalid. The dual-species plasma will be generated by resonantly photo-ionizing laser-cooled Yb and Ca atoms in the same magneto-optical trap. Laser-induced fluorescence measurements will be used to measure the time-evolving ion velocity distribution for each ion species simultaneously. By delaying the ionization of one species relative to the other, the time scale for full energy relaxation can be determined. State-of-the-art molecular dynamics simulations will be performed that match the density, stoichiometry, and geometry of the experiments. The calculations will provide a first-principles description of collision processes by directly integrating many-body trajectories. Arbitrarily complicated orbits will be computed self-consistently with dynamical many-body screening. The many-body phase dynamics will be inverted to yield highly accurate effective Coulomb logarithms, providing important information back to the high energy density community. This project will support one graduate student per year for three years at BYU, two undergraduate students per year at BYU, two undergraduate students per year at WU, and one post-doc per year for two years at NMC.", "AwardID" -> "1500363", "Institution" -> Entity["NSFInstitution", "NewMexicoConsortium"], "Investigators" -> {Entity["NSFInvestigator", "MichaelMurillo"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500363&HistoricalAwards=false"], "KeywordTally" -> {{"collisions", 9}, {"energy", 7}, {"project", 6}, {"ions", 5}, {"measure", 5}, {"plasma", 5}, {"high", 4}, {"ion", 4}, {"plasmas", 4}, {"students", 4}, {"used", 4}, {"work", 4}, {"year", 4}, {"accurate", 3}, {"atoms", 3}, {"-body", 3}, {"collision", 3}, {"computations", 3}, {"crash", 3}, {"density", 3}, {"proposed", 3}, {"simulations", 3}, {"violent", 3}, {"BYU", 2}, {"collaborative", 2}, {"compared", 2}, {"Coulomb", 2}, {"data", 2}, {"directly", 2}, {"dual-species", 2}, {"dynamics", 2}, {"electrical", 2}, {"force", 2}, {"fundamental", 2}, {"graduate", 2}, {"important", 2}, {"ion-ion", 2}, {"measurements", 2}, {"new", 2}, {"New", 2}, {"relaxation", 2}, {"research", 2}, {"results", 2}, {"scientists", 2}, {"second", 2}, {"slow", 2}, {"small", 2}, {"species", 2}, {"speed", 2}, {"state---art", 2}, {"undergraduate", 2}, {"University", 2}, {"years", 2}}|>, "1500365" -> <|"AwardTitle" -> "EAGER: Systematic and Scalable Testing of Concurrent Software in the Cloud", "AwardEffectiveDate" -> DateObject[{2015, 2, 15}], "AwardExpirationDate" -> DateObject[{2016, 7, 31}], "AwardAmount" -> Quantity[65559, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "05010000", "ProgramOfficer" -> "Sol J. Greenspan", "Abstract" -> "While multicore and many core and GPU processors increase computing speed, the concurrent and parallel programs written for them are increasingly complex, hard to verify, and difficult to test. So-called \"concurrency bugs\" are very hard to find, because of the huge number of thread interleavings that need to be examined to find the circumstances in which a bug might occur. Techniques for finding bugs in sequential programs do not scale to concurrent programs, especially for programs with data inputs and shared memory, which require more rigor and exhaustive testing. The project will investigate an approach that combines symbolic execution with a form of schedule exploration to find efficient solutions. Scalability is pursued by seeking to parallelize the execution on a cloud platform, which is a step toward a cloud service for concurrent software testing. There is a dire need for tools capable of doing scalable and efficient testing of concurrent programs, which will have a high impact on software quality and correctness if implemented in a widely available service. This EAGER grant will explore the feasibility of this high-risk, potentially high-reward approach.", "AwardID" -> "1500365", "Institution" -> Entity["NSFInstitution", "WesternMichiganUniversity"], "Investigators" -> {Entity["NSFInvestigator", "ZijiangYang"]}, "ProgramElements" -> {{"Code" -> "7798", "Text" -> "SOFTWARE & HARDWARE FOUNDATION"}}, "ProgramReferences" -> {{"Code" -> "7916", "Text" -> "EAGER"}, {"Code" -> "7944", "Text" -> "SOFTWARE ENG & FORMAL METHODS"}}, "Directorate" -> "Direct For Computer & Info Scie & Enginr", "Division" -> "Division of Computing and Communication Foundations", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500365&HistoricalAwards=false"], "KeywordTally" -> {{"programs", 5}, {"concurrent", 4}, {"testing", 3}, {"approach", 2}, {"bugs", 2}, {"cloud", 2}, {"efficient", 2}, {"execution", 2}, {"hard", 2}, {"need", 2}, {"service", 2}, {"software", 2}}|>, "1500367" -> <|"AwardTitle" -> "Solidification Cracking in Welds of Aluminum Alloys", "AwardEffectiveDate" -> DateObject[{2015, 7, 15}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[309243, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03070000", "ProgramOfficer" -> "Diana Farkas", "Abstract" -> "Non-Technical Abstract \nAluminum alloys are increasingly used for vehicle weight reduction, and arc welding is the most versatile process for welding them. However, aluminum alloys are susceptible to cracking during solidification, which is called solidification cracking in welding and hot tearing in casting. In the present project a simple new index is presented to predict the relative crack susceptibility of aluminum alloys and how it is affected by the filler metals used for welding. The index can be calculated easily using commercially available software packages and databases for aluminum alloys. The index can be a useful guide to selecting existing welding filler metals or searching for new ones to avoid solidification cracking in aluminum welds. The index can also be applied to aluminum casting, where hot tearing is a serious problem. The project seeks to provide an opportunity for a Hispanic graduate student to learn welding, aluminum alloys, and failure analysis of welded components.\n\nTechnical Abstract\nAn alloy exists in the weak semisolid state during solidification, with solid grains separated by thin liquid films during the terminal stage of solidification. The semisolid can crack along grain boundaries under the tension induced during welding or casting. How the fraction solid fs of the semisolid increases as temperature T drops during solidification can affect the crack susceptibility significantly, and it differs significantly from alloy to alloy. Unlike previous studies, the present project considers the grain boundary, where cracking occurs. It considers: 1. the tension to separate neighboring grains to cause cracking, 2. the growth of neighboring grains toward each other to bond together to resist cracking, and 3. the liquid feeding to fill the boundary between neighboring grains to resist cracking. Based on the criterion required for cracking to occur at the grain boundary, a simple new index is deduced to predict the relative crack susceptibility of aluminum alloys and the effectiveness of welding filler metals in reducing the crack susceptibility. The index can be determined from the steepness of the curve of T vs. the square root of fs, which can be calculated easily using commercial software packages and databases. A simple new test is developed to assess the relative crack susceptibility of commercial aluminum alloys in welding and to verify the new criterion and index. To cause cracking during the test, the semisolid region of the weld alone is pulled at a slow rate similar to that occurring naturally during welding, instead of bending the workpiece suddenly during welding, which is done in the most widely used test and which induces unrealistically fast and high tension in the semisolid region.", "AwardID" -> "1500367", "Institution" -> Entity["NSFInstitution", "UniversityOfWisconsin-Madison"], "Investigators" -> {Entity["NSFInvestigator", "SindoKou"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Materials Research", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500367&HistoricalAwards=false"], "KeywordTally" -> {{"welding", 11}, {"cracking", 9}, {"aluminum", 8}, {"alloys", 7}, {"index", 7}, {"crack", 6}, {"solidification", 6}, {"new", 5}, {"semisolid", 5}, {"susceptibility", 5}, {"grains", 4}, {"alloy", 3}, {"boundary", 3}, {"casting", 3}, {"filler", 3}, {"grain", 3}, {"metals", 3}, {"neighboring", 3}, {"project", 3}, {"relative", 3}, {"simple", 3}, {"tension", 3}, {"test", 3}, {"used", 3}, {"calculated", 2}, {"cause", 2}, {"commercial", 2}, {"considers", 2}, {"criterion", 2}, {"databases", 2}, {"easily", 2}, {"fs", 2}, {"hot", 2}, {"liquid", 2}, {"packages", 2}, {"predict", 2}, {"present", 2}, {"region", 2}, {"resist", 2}, {"significantly", 2}, {"software", 2}, {"solid", 2}, {"T", 2}, {"tearing", 2}, {"using", 2}}|>, "1500368" -> <|"AwardTitle" -> "Illinois LSAMP Bridge to the Doctorate at the University of Illinois at Chicago (2015-2017)", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Martha L. James", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the Science, Technology, Engineering, and Mathematics (STEM) workforce through the development of highly competitive students from groups historically underrepresented in STEM disciplines: African-Americans, Alaska Natives, American Indians, Hispanic Americans, Native Hawaiians, and Native Pacific Islanders. The goal of the LSAMP Bridge to the Doctorate (BD) Activity is to increase the quantity and quality of STEM graduate students from underrepresented populations, with emphasis on Ph.D. matriculation and completion. For the U.S. to remain globally competitive, it is vital that it taps into the talent of all its citizens and provides exceptional educational preparedness in STEM areas that underpin the knowledge-based economy. BD programs implemented in the nation's institutions of higher education contribute to addressing one of the objectives in NSF's 2014-2018 Strategic Plan, namely to \"integrate education and research to support development of a diverse STEM workforce with cutting-edge capabilities.\" The Illinois Louis Stokes Alliance for Minority Participation (ILSAMP) is led by Chicago State University, which is a Predominantly Black University and will host the 2015-2017 cohort of BD Fellows, with the University of Illinois at Chicago (UIC) as the main implementation campus. UIC will offer a comprehensive program that includes rigorous academic preparation and research training experiences as well as mentorship and professional development activities. Since the strategies implemented at UIC will result in the production of well-trained, highly-skilled STEM Professionals from underrepresented groups, the project will contribute significantly to increasing the diversity and representation in academia and the STEM workforce, thereby ensuring the nation's global competitiveness. \n\nSince starting in 2006, the ILSAMP BD at UIC has produced 22 STEM PhDs out of its 42 fellows from three cohorts. The Illinois LSAMP BD Program at UIC will continue to produce more STEM PhDs following the four primary objectives of the program: \n1. To recruit twelve highly motivated students from LSAMP campuses across the nation; \n2. To prepare matriculating BD Fellows to study and train towards the PhD; \n3. To facilitate activities that will encourage BD Fellows to persist in PhD studies; and \n4. To implement a series of activities designed to enhance the education and training of ILSAMP BD Fellows and help them transition to postdoctoral fellowships, placement in the academy, or other positions requiring doctoral level STEM education.", "AwardID" -> "1500368", "Institution" -> Entity["NSFInstitution", "ChicagoStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "LeRoyJonesII"], Entity["NSFInvestigator", "AngelaHenderson"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500368&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 10}, {"BD", 8}, {"UIC", 5}, {"education", 4}, {"Fellows", 4}, {"LSAMP", 4}, {"activities", 3}, {"development", 3}, {"Illinois", 3}, {"ILSAMP", 3}, {"program", 3}, {"students", 3}, {"underrepresented", 3}, {"University", 3}, {"workforce", 3}, {"Chicago", 2}, {"competitive", 2}, {"contribute", 2}, {"groups", 2}, {"highly", 2}, {"implemented", 2}, {"Louis", 2}, {"Minority", 2}, {"nation's", 2}, {"Native", 2}, {"objectives", 2}, {"Participation", 2}, {"PhD", 2}, {"PhDs", 2}, {"research", 2}, {"Stokes", 2}, {"training", 2}}|>, "1500375" -> <|"AwardTitle" -> "CyberWatch West: Securing the Cyber West", "AwardEffectiveDate" -> DateObject[{2015, 10, 1}], "AwardExpirationDate" -> DateObject[{2018, 9, 30}], "AwardAmount" -> Quantity[2202387, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11040100", "ProgramOfficer" -> "R. Corby Hovis", "Abstract" -> "Keeping computers and information systems secure is a major challenge. Business, industry, and government need well-prepared technicians who can prevent, detect, and investigate cybersecurity breaches, and the growth of cyber-threats has created a need for many more workers who have appropriate, specific knowledge and skills. To address these needs, CyberWatch West (CWW; http://cyberwatchwest.org), an Advanced Technological Education (ATE) regional center, will continue its activities that are strengthening and expanding cybersecurity education in the Western region of the United States. This area is home to many high-tech companies, utilities, government agencies, and nonprofit organizations, which need a healthy supply of employees with cybersecurity knowledge and skills at all levels. CWW's cybersecurity education programs, hands-on cyber competitions and training workshops, approaches to faculty and student development, and industry engagement initiatives are proven models that should be shared broadly across the West and the nation. In cooperation with industry and government partners, CWW will educate students to fill thousands of job openings in cybersecurity and will thereby address national needs for the security of critical infrastructure, defense, healthcare, and commerce.\n\nCWW was previously funded through NSF Awards DUE-1104278 and DUE-1361636. The center's mission is to strengthen the cybersecurity workforce in the Western United States by providing solutions to address the limited resources at community colleges through innovative curriculum development; building an online community for faculty professional growth and mentoring; creating a developmental pathway of competitions that facilitate growth of students' cybersecurity skills; and supporting other efforts at the state, regional, and national levels to develop and disseminate cybersecurity programs. The center will disseminate its model cybersecurity education programs throughout a 14-state region; expand curriculum development, faculty professional development, and student development opportunities; and strengthen and sustain industry partnerships to ensure up-to-date curricula as well as student internships and employment. In particular, CWW will support institutions seeking the National Center of Academic Excellence in Information Assurance 2-Year Education (CAE2Y) designation. The center will develop model curricula that meet CAE2Y Knowledge Unit (KU) criteria and National Initiative for Cybersecurity Education (NICE) criteria addressing workforce readiness. Expanding CWW's past work on \"2 + 2 + 2\" educational pathways, the center will develop a cybersecurity Transfer Model Curriculum (TMC) to facilitate automatic transfer for California community college students to universities in the California State University system. CWW will further serve college faculty in the region by addressing new topics and content in cybersecurity via webinars, workshops, the CWW website, and an innovative faculty mentoring program.", "AwardID" -> "1500375", "Institution" -> Entity["NSFInstitution", "WhatcomCommunityCollege"], "Investigators" -> {Entity["NSFInvestigator", "DanManson"], Entity["NSFInvestigator", "NancyJones"], Entity["NSFInvestigator", "TonyCoulson"], Entity["NSFInvestigator", "CorrinneSande"]}, "ProgramElements" -> {{"Code" -> "1668", "Text" -> "FED CYBER SERV: SCHLAR FOR SER"}, {"Code" -> "7412", "Text" -> "ADVANCED TECH EDUCATION PROG"}}, "ProgramReferences" -> {{"Code" -> "1032", "Text" -> "ADVANCED TECHNOLOGY EDUCATION"}, {"Code" -> "7434", "Text" -> "CNCI"}, {"Code" -> "9178", "Text" -> "UNDERGRADUATE EDUCATION"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Undergraduate Education", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500375&HistoricalAwards=false"], "KeywordTally" -> {{"cybersecurity", 11}, {"CWW", 5}, {"development", 5}, {"faculty", 5}, {"center", 4}, {"industry", 4}, {"2", 3}, {"address", 3}, {"community", 3}, {"develop", 3}, {"education", 3}, {"Education", 3}, {"government", 3}, {"growth", 3}, {"need", 3}, {"programs", 3}, {"region", 3}, {"skills", 3}, {"student", 3}, {"students", 3}, {"addressing", 2}, {"CAE2Y", 2}, {"California", 2}, {"college", 2}, {"competitions", 2}, {"criteria", 2}, {"curricula", 2}, {"curriculum", 2}, {"CWW's", 2}, {"disseminate", 2}, {"facilitate", 2}, {"innovative", 2}, {"knowledge", 2}, {"levels", 2}, {"mentoring", 2}, {"model", 2}, {"national", 2}, {"National", 2}, {"needs", 2}, {"professional", 2}, {"regional", 2}, {"States", 2}, {"strengthen", 2}, {"United", 2}, {"West", 2}, {"Western", 2}, {"workforce", 2}, {"workshops", 2}}|>, "1500376" -> <|"AwardTitle" -> "Collaborative Research: Plasma Physics At Small Coulomb Logarithms", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[135000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "This collaborative research project will advance fundamental understanding of how groups of high speed ions crash into and interact with each other. One can measure just how violent a collision is by comparing the energy of the crashing high-speed ions with the electrical force between them. The most violent ion collisions, the ones that are most important both for extending our scientific knowledge and for developing technological applications, are very difficult to measure or calculate. They occur in extremely hot and very dense gases of charged particles called plasmas. In this project, new ideas will be used to measure and understand these collisions. Lasers will be used to slow atoms from speeds of nearly 1000 meters per second to a crawl of about an inch per second; and then to turn these slow atoms into ions. Additional lasers will then be used to measure how these ions crash into each other. The ions in these slow-motion collisions have the same amount of crash energy compared to the ion-ion electrical force, which means that the collision results can be directly compared to similar collisions at any energy. This project will use state-of-the-art large-scale computer simulations to make movies of the ion-ion collisions and compare these to the experimental measurements. When the computations are proven to be sufficiently accurate, approximations will be gradually introduced and tested in order to speed up the computations. These results will then set the standard for accurate and fast computations of ion collisions in plasmas. Several students will work on this project: Undergraduate and graduate students and post-doctoral scientists will work closely with expert scientists at Willamette University (Oregon), Brigham Young University (Utah), and the New Mexico Consortium (New Mexico).\n\nThe proposed collaborative research project will investigate energy relaxation in a system in which the value of the Coulomb logarithm is small. This is typical of high-energy-density systems, where violent small-impact-parameter collisions result in large particle deflections. Understanding these collisions is a priority for advancing fundamental plasma physics and for accurately modeling small impact parameter collisions in high energy density plasmas. The proposed work will generate high quality data in plasma regimes where traditional diagnostics are limited. The proposed work will combine data from a new dual-species ultracold neutral plasma experiment and state-of-the-art simulations to study temperature equilibration in moderately coupled plasmas, in which classic plasma assumptions are invalid. The dual-species plasma will be generated by resonantly photo-ionizing laser-cooled Yb and Ca atoms in the same magneto-optical trap. Laser-induced fluorescence measurements will be used to measure the time-evolving ion velocity distribution for each ion species simultaneously. By delaying the ionization of one species relative to the other, the time scale for full energy relaxation can be determined. State-of-the-art molecular dynamics simulations will be performed that match the density, stoichiometry, and geometry of the experiments. The calculations will provide a first-principles description of collision processes by directly integrating many-body trajectories. Arbitrarily complicated orbits will be computed self-consistently with dynamical many-body screening. The many-body phase dynamics will be inverted to yield highly accurate effective Coulomb logarithms, providing important information back to the high energy density community. This project will support one graduate student per year for three years at BYU, two undergraduate students per year at BYU, two undergraduate students per year at WU, and one post-doc per year for two years at NMC.", "AwardID" -> "1500376", "Institution" -> Entity["NSFInstitution", "BrighamYoungUniversity"], "Investigators" -> {Entity["NSFInvestigator", "ScottBergeson"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500376&HistoricalAwards=false"], "KeywordTally" -> {{"collisions", 9}, {"energy", 7}, {"project", 6}, {"ions", 5}, {"measure", 5}, {"plasma", 5}, {"high", 4}, {"ion", 4}, {"plasmas", 4}, {"students", 4}, {"used", 4}, {"work", 4}, {"year", 4}, {"accurate", 3}, {"atoms", 3}, {"-body", 3}, {"collision", 3}, {"computations", 3}, {"crash", 3}, {"density", 3}, {"proposed", 3}, {"simulations", 3}, {"violent", 3}, {"BYU", 2}, {"collaborative", 2}, {"compared", 2}, {"Coulomb", 2}, {"data", 2}, {"directly", 2}, {"dual-species", 2}, {"dynamics", 2}, {"electrical", 2}, {"force", 2}, {"fundamental", 2}, {"graduate", 2}, {"important", 2}, {"ion-ion", 2}, {"measurements", 2}, {"new", 2}, {"New", 2}, {"relaxation", 2}, {"research", 2}, {"results", 2}, {"scientists", 2}, {"second", 2}, {"slow", 2}, {"small", 2}, {"species", 2}, {"speed", 2}, {"state---art", 2}, {"undergraduate", 2}, {"University", 2}, {"years", 2}}|>, "1500377" -> <|"AwardTitle" -> "UNS: Multi-scale Simulations of Branched Thread-like Micelles", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[320548, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07020000", "ProgramOfficer" -> "William Olbricht", "Abstract" -> "CBET - 1500377\nPI: Larson, Ronald\n\nSurfactants are used in many household, medical, and industrial products. Surfactant molecules in solution can spontaneously assemble into structures, which can strongly influence the properties of the liquid. This project will develop a theory to predict the properties of solutions of thread-like micelles, which are long flexible surfactant structures. The particular focus of the proposed work is to explore the role of micelle branching in the behavior of these interesting solutions. The results of the work will be incorporated into an open source software package that will be made freely available for use in the industrial formulation of surfactant solutions. Students involved in the research will have the opportunity to gain experience in industrially-related research through internships at collaborating companies.\n\nA detailed, quantitative theory will be developed to predict the linear rheology of solutions of branched threadlike micelles, including effects of reptation (or sliding) of the micelles through the entanglement network, as well as fluctuations in the \"primitive path\" of the micelles, micelle breakage and rejoining, formation and breakage of network junctions, and other relaxation phenomena. These phenomena will be modeled using a \"Pointer Algorithm\" developed by the PI that accounts for micelle relaxation phenomena, but not for micellar branching. The incorporation of branch formation will represent a major advance in understanding the dynamics and rheology of surfactant solutions. This methodology will provide accurate estimates of micelle lengths, breakage rates, and rates of formation and breakage of branch points, and the number of branches per micelle, extracted from rheology data by fits of this data to predictions of the Pointer Algorithm.", "AwardID" -> "1500377", "Institution" -> Entity["NSFInstitution", "UniversityOfMichiganAnnArbor"], "Investigators" -> {Entity["NSFInvestigator", "RonaldLarson"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Chem, Bioeng, Env, & Transp Sys", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500377&HistoricalAwards=false"], "KeywordTally" -> {{"micelle", 5}, {"solutions", 5}, {"breakage", 4}, {"micelles", 4}, {"formation", 3}, {"phenomena", 3}, {"rheology", 3}, {"surfactant", 3}, {"Algorithm", 2}, {"branch", 2}, {"branching", 2}, {"data", 2}, {"developed", 2}, {"industrial", 2}, {"network", 2}, {"Pointer", 2}, {"predict", 2}, {"properties", 2}, {"rates", 2}, {"relaxation", 2}, {"research", 2}, {"structures", 2}, {"theory", 2}, {"work", 2}}|>, "1500381" -> <|"AwardTitle" -> "Methods and Applications for Bilinear Operators", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[115463, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The subject matter of this project belongs to the realm of bilinear Fourier analysis. After the pioneering work of Joseph Fourier in the first decades of the nineteenth century, one is now familiar with the process of decomposing a signal or function into its elementary frequency components (analysis) as well as with the reverse process of superposing individual frequency components to form a single signal (synthesis). Fourier analysis thus acts in a way similar to a prism, which allows one to see the individual color components of a beam of light. Along these lines, when two functions or signals coexist, their frequency components interact and this phenomenon plays a key role in the study of certain partial differential equations that arise, for instance, in optics, quantum mechanics, and fluid dynamics. In the field of bilinear Fourier analysis, tools are developed to model the behavior and interaction of two signals by decomposing each one into their constituent frequencies, separating each decomposition into low and high frequencies, and studying the interplay between the low-low, high-low, and high-high frequencies from each decomposition. This project will also contribute to the integration of research and education at the postdoctoral, graduate, and undergraduate levels, to advancing discovery, to forming human resources, and to developing academic curricula.\n\nMotivated by the study of commutators, bilinear Leibniz-type rules, paraproducts, and related topics in analysis and partial differential equations, the research activities of this project aim at developing methods in bilinear Fourier analysis to advance the theory of bilinear pseudo-differential operators and their applications. In particular, problems to be addressed include the description of the mapping properties, in the scales of Lebesgue, Besov, and Triebel-Lizorkin spaces, of bilinear pseudodifferential operators with symbols in certain critical classes.", "AwardID" -> "1500381", "Institution" -> Entity["NSFInstitution", "KansasStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "VirginiaNaibo"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500381&HistoricalAwards=false"], "KeywordTally" -> {{"analysis", 6}, {"bilinear", 6}, {"Fourier", 5}, {"components", 4}, {"frequencies", 3}, {"frequency", 3}, {"project", 3}, {"certain", 2}, {"decomposing", 2}, {"decomposition", 2}, {"developing", 2}, {"differential", 2}, {"equations", 2}, {"individual", 2}, {"operators", 2}, {"partial", 2}, {"process", 2}, {"research", 2}, {"signal", 2}, {"signals", 2}, {"study", 2}}|>, "1500382" -> <|"AwardTitle" -> "Geometry of Sets and Measures", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[79496, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Geometric measure theory is a field of mathematics that developed starting in the 1920s and 1930s, growing out of a practical need to describe nonsmooth phenomena such as the formation of corners in soap bubble clusters. The term \"measure\" refers to an abstract generalization of length, area, or volume, which assigns a size value to every mathematical set. Traditional outlets for geometric measure theory, such as the calculus of variations and geometric analysis, have expanded in recent decades to include partial differential equations and harmonic analysis. The widespread utility and current use of geometric measure theory in different areas of analysis justifies its continued development. The proposed investigation on the geometry of sets and measures seeks to develop new techniques that will expand the toolbox that geometric measure theory provides for researchers in adjacent areas in analysis and geometry.\n\nThis project focuses on two groups of questions about the geometry of sets and measures in Euclidean space. The first group of questions concerns rectifiable measures, one of the core objects of study in geometric measure theory. Specifically, these questions are aimed at increased understanding of rectifiable measures in the absence of a standing regularity assumption that has been assumed in the past. The main approach entails adapting quantitative techniques developed in the 1990s by Jones and David-Semmes to study the qualitative rectifiability of measures. The second group of questions are designed to examine the geometry of Reifenberg-type sets, which are sets that can be approximated at all locations and scales by one or more kinds of model sets. Instances where Reifenberg-type sets occur include geometric minimization problems and free boundary problems for elliptic partial differential equations. A general goal of this inquiry is to determine in what situations and to what extent good properties of solutions to problems in ideal models (smooth settings) persist under controlled perturbation (weak regularity).", "AwardID" -> "1500382", "Institution" -> Entity["NSFInstitution", "UniversityOfConnecticut"], "Investigators" -> {Entity["NSFInvestigator", "MatthewBadger"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500382&HistoricalAwards=false"], "KeywordTally" -> {{"geometric", 6}, {"measure", 6}, {"sets", 6}, {"measures", 5}, {"theory", 5}, {"analysis", 4}, {"questions", 4}, {"geometry", 3}, {"problems", 3}, {"areas", 2}, {"developed", 2}, {"differential", 2}, {"equations", 2}, {"group", 2}, {"include", 2}, {"partial", 2}, {"rectifiable", 2}, {"regularity", 2}, {"Reifenberg-type", 2}, {"study", 2}, {"techniques", 2}}|>, "1500386" -> <|"AwardTitle" -> "Quantum Diffusion in Fluctuating Media", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[120000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "The main focus of this project is the analysis of wave motion in a disordered environment. In a broader context, the research is aimed at answering a basic scientific question: \"What are the effects of disorder?\" This is a fundamental question relevant to any mathematical model, even one in which disorder is not explicitly included. After all, any real world system is subject to a small amount of noise, and experience shows that even weak disorder may have a profound effect on the behavior of the system. The equations studied in this project arise in the theory of electrical conduction in disordered materials, but are of general interest because of the fundamental nature of both wave motion and disorder. Progress in understanding the solutions to these equations will improve basic understanding of models of theoretical physics and applied mathematics. In addition, a central goal of the research is pedagogical: to introduce undergraduate and graduate students to a fundamental subject and convey to them that mathematics is a vibrant, growing field. \n\nThe project will proceed through a program of research on the effects of disorder in physical models. A key goal is to analyze the diffusion of waves in a weakly disordered medium over arbitrarily long times. There is a rich non-rigorous theory of the weakly disordered regime in the physics literature based on heuristic analyses and uncontrolled, renormalized perturbation theory which suggests that waves propagate diffusively, characterized by spreading of wave packets over a distance proportional to the square root of t in time t. However, we are far from having a rigorous analysis of the mathematics involved. A major challenge is that diffusive propagation does not occur for waves in a non-random medium. Thus, a naive approach in which the disorder is incorporated perturbatively has not worked, indeed in the physics literature the problem is attacked with renormalized perturbation theory. In recent years the PI and various post-doc and student collaborators have considered the problem of wave diffusion in time-dependent random media, with the time dependence generated by a Markov process. For such models the diffusive propagation, e.g., for the tight binding Schrödinger equation, can be established by spectral analysis. One aim of the present project is to approach the time independent equation as a perturbation of these time dependent equations, which have the virtue of sharing the expected qualitative behavior.", "AwardID" -> "1500386", "Institution" -> Entity["NSFInstitution", "MichiganStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "JeffreySchenker"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500386&HistoricalAwards=false"], "KeywordTally" -> {{"disorder", 6}, {"disordered", 4}, {"project", 4}, {"theory", 4}, {"time", 4}, {"wave", 4}, {"analysis", 3}, {"equations", 3}, {"fundamental", 3}, {"mathematics", 3}, {"models", 3}, {"perturbation", 3}, {"physics", 3}, {"research", 3}, {"waves", 3}, {"approach", 2}, {"basic", 2}, {"behavior", 2}, {"diffusion", 2}, {"diffusive", 2}, {"effects", 2}, {"equation", 2}, {"goal", 2}, {"literature", 2}, {"medium", 2}, {"motion", 2}, {"problem", 2}, {"propagation", 2}, {"question", 2}, {"renormalized", 2}, {"subject", 2}, {"system", 2}, {"t", 2}, {"understanding", 2}, {"weakly", 2}}|>, "1500387" -> <|"AwardTitle" -> "Classifying subfactors and fusion categories", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[144773, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Symmetry plays an important role in mathematics and in the biological and physical sciences. For example, a theorem of Emmy Noether states that symmetries of physical systems, like time and space translation, correspond to conserved quantities, like energy and momentum, respectively. Von Neumann, in his study of quantum mechanics, discovered that certain operator algebras on Hilbert space describe symmetries of quantum systems. These von Neumann algebras are built from basic building blocks called factors. A subfactor is an inclusion of factors, and its representation theory encodes quantum symmetries. In the classical setting, the symmetries of a particular object form a group, like the collection of symmetries of a square or of a molecule. When one passes from the classical setting to the quantum setting, these groups are replaced by so-called quantum groups and tensor categories. Unitary tensor categories arise naturally in the study of subfactors, and in return, subfactor theory provides a wealth of techniques for classification and construction of examples. Moreover, the quantum doubles of unitary fusion categories are unitary modular categories, which are vital to research in topological phases of matter and topological quantum computation.\n\nThe first aim of this project is the classification of subfactors and fusion categories. The small index subfactor classification program has seen recent success classifying up to index five, and the principal investigator will raise this index bound slightly above five. To raise the bound even further, up towards six, new techniques and obstructions are necessary. The project will also develop more techniques for studying infinite index subfactors, where there are relatively few results. The second aim is developing deeper connections between subfactors and free probability, C*-algebras, noncommutative geometry, and conformal field theory (CFT). Recent work of Guionnet, Jones, and Shlyakhtenko developed a connection between subfactors, random matrices, and free probability. With Hartglass, the principal investigator developed this connection, discovering new connections to C*-algebras and noncommutative geometry via work of Pimsner and Voiculescu. The project will continue to investigate these new developments. Finally, conformal nets on the circle intimately relate subfactors and CFT. In joint work with Henriques and Tener, the principal investigator will study conformal planar algebras, which are a common generalization of Jones's subfactor planar algebras and genus-zero Segal CFT. Tener and the principal investigator anticipate a classification in terms of module categories for the representation category of this CFT. They also conjecture the subfactor/planar algebra duality extends to a duality between conformal planar algebras and certain morphisms in the 3-category of conformal nets.", "AwardID" -> "1500387", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-LosAngeles"], "Investigators" -> {Entity["NSFInvestigator", "DavidPenneys"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500387&HistoricalAwards=false"], "KeywordTally" -> {{"algebras", 7}, {"quantum", 7}, {"categories", 6}, {"subfactors", 6}, {"conformal", 5}, {"subfactor", 5}, {"symmetries", 5}, {"CFT", 4}, {"classification", 4}, {"index", 4}, {"investigator", 4}, {"planar", 4}, {"principal", 4}, {"like", 3}, {"new", 3}, {"project", 3}, {"setting", 3}, {"study", 3}, {"techniques", 3}, {"theory", 3}, {"work", 3}, {"aim", 2}, {"bound", 2}, {"C", 2}, {"certain", 2}, {"classical", 2}, {"connection", 2}, {"connections", 2}, {"developed", 2}, {"duality", 2}, {"factors", 2}, {"five", 2}, {"free", 2}, {"fusion", 2}, {"geometry", 2}, {"groups", 2}, {"nets", 2}, {"Neumann", 2}, {"noncommutative", 2}, {"physical", 2}, {"probability", 2}, {"raise", 2}, {"representation", 2}, {"space", 2}, {"systems", 2}, {"Tener", 2}, {"tensor", 2}, {"topological", 2}, {"unitary", 2}}|>, "1500389" -> <|"AwardTitle" -> "Ergodic Theory of Nonamenable Group Actions", "AwardEffectiveDate" -> DateObject[{2015, 5, 15}], "AwardExpirationDate" -> DateObject[{2018, 4, 30}], "AwardAmount" -> Quantity[245851, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "Classical dynamics studies how systems change in time. Ergodic theory focuses on the statistical behavior of dynamical systems. Applications of ergodic theory are widespread: from traffic modelling to aerospace engineering and population dynamics. It is natural and of practical importance to generalize the role of time in a dynamical system to more complicated groups of symmetries. This generalized notion of dynamics leads to applications in statistical mechanics, number theory, and geometry. However, new tools are needed, especially in the particular case when the group of symmetries is non nonamenable, which means that boundary phenomena are too significant to be safely ignored (unlike intervals in the integers or real numbers). Nonamenable groups naturally arise in many parts of mathematics, such as geometry and number theory. This project is concerned with developing the tools needed to analyze the ergodic theory of nonamenable group actions. \n\nThere are five specific goals. The first is to continue developing sofic entropy theory. This is a vast generalization of Kolmogorov-Sinai entropy to actions of sofic groups, a class of groups that contains all amenable groups and residually finite groups. One major aim of this research is to determine to what extent Ornstein theory can be extended beyond actions of amenable groups. The second goal is to establish pointwise ergodic theorems for geometrically defined groups (e.g. Lie groups, CAT(0) cubulated groups, relatively hyperbolic groups) using techniques recently discovered by the PI and Amos Nevo. The third goal is to import tools from geometric group theory into the study of measured equivalence relations. The fourth goal is to continue to analyzing the structure of the space of weak equivalence classes of actions of a given group. This space serves as a classifying object for the ways in which the Rokhlin Lemma fails for nonamenable groups. Because the Rokhlin Lemma is of crucial importance in Ornstein theory, this topic is intimately connected with the first goal. The fifth goal is to continue clarifying what the space of stationary actions of a given group \"looks like.'' One major focus is on new constructions of stationary actions (via invariant random subgroups or measured equivalence relations). Another is on generic behavior of stationary actions. Yet another is to apply the new techniques to the study of harmonic functions and random walks; topics deeply connected with stationary actions.", "AwardID" -> "1500389", "Institution" -> Entity["NSFInstitution", "UniversityOfTexasAtAustin"], "Investigators" -> {Entity["NSFInvestigator", "LewisBowen"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500389&HistoricalAwards=false"], "KeywordTally" -> {{"groups", 12}, {"theory", 9}, {"actions", 8}, {"goal", 5}, {"group", 5}, {"stationary", 4}, {"continue", 3}, {"dynamics", 3}, {"equivalence", 3}, {"ergodic", 3}, {"new", 3}, {"nonamenable", 3}, {"space", 3}, {"tools", 3}, {"amenable", 2}, {"behavior", 2}, {"connected", 2}, {"developing", 2}, {"dynamical", 2}, {"entropy", 2}, {"geometry", 2}, {"given", 2}, {"importance", 2}, {"Lemma", 2}, {"major", 2}, {"measured", 2}, {"needed", 2}, {"number", 2}, {"Ornstein", 2}, {"random", 2}, {"relations", 2}, {"Rokhlin", 2}, {"sofic", 2}, {"statistical", 2}, {"study", 2}, {"symmetries", 2}, {"systems", 2}, {"techniques", 2}, {"time", 2}}|>, "1500400" -> <|"AwardTitle" -> "The Linearized Monge-Ampere Equation and Applications in Nonlinear, Geometric Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[100000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This research project focuses on fine properties of solutions to the linearized Monge-Ampere equation and their applications to nonlinear, geometric partial differential equations (PDEs) of great importance in geometric, mechanical, and economic contexts. The Monge-Ampere type equations arise naturally in optimal transportation problems in economics and in traffic network planning in cities, in the design of reflector antennae in geometric optics, and in the semi-geostrophic equations of meteorology. The project covers a broad class of PDEs where key structural quantities could be possibly extremely small (degenerate) or extremely large (singular). The main goal of the project aims at discovering new underlying principles and correct perspectives on these equations in order to develop innovative tools and methodologies to tackle them. Understanding deeper properties of affine maximal surface equations studied in this project will help design faster algorithms in architectural free-form structures, in computer graphics, and in visualization where convex objects are involved. In addition to applications, the successful analysis of PDEs investigated in this project will reveal deep and interesting connections between different areas of mathematics such as analysis, PDEs, the calculus of variations, geometry, and fluid mechanics, thereby augmenting the fruitful interaction among them.\n\nThis project, in the field of analysis and partial differential equations (PDEs), focuses on regularity properties of solutions to the linearized Monge-Ampere (LMA) equation and their applications to nonlinear, geometric PDEs. The linearized Monge-Ampere equation arises in several fundamental problems of current interest in computer graphics, affine geometry, complex geometry, fluid mechanics, and economics. The purpose of this project is to obtain fine and higher order boundary regularity properties of the LMA equation and apply them to tackle several outstanding problems in analysis, geometry, and PDEs. More specifically, the objectives of the project are to: investigate sharp boundary regularity for the LMA equation; apply these regularity results to understand qualitative properties of several interesting but highly challenging nonlinear, fourth-order geometric equations such as the second boundary value problems for the affine maximal surface and Abreu's equations, and finally resolve the outstanding open problem on global smoothness of eigenfunctions to the Monge-Ampere operator. The techniques used in attacking the problems under study in this project include perturbation arguments, localization techniques, covering arguments, partial Legendre transform, geometry of the Monge-Ampere equation, and also harmonic analysis on homogeneous spaces.", "AwardID" -> "1500400", "Institution" -> Entity["NSFInstitution", "IndianaUniversity"], "Investigators" -> {Entity["NSFInvestigator", "NamLe"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500400&HistoricalAwards=false"], "KeywordTally" -> {{"project", 9}, {"equations", 8}, {"PDEs", 7}, {"equation", 6}, {"Monge-Ampere", 6}, {"analysis", 5}, {"geometric", 5}, {"geometry", 5}, {"problems", 5}, {"properties", 5}, {"regularity", 4}, {"affine", 3}, {"applications", 3}, {"boundary", 3}, {"linearized", 3}, {"LMA", 3}, {"nonlinear", 3}, {"partial", 3}, {"apply", 2}, {"arguments", 2}, {"computer", 2}, {"design", 2}, {"differential", 2}, {"economics", 2}, {"extremely", 2}, {"fine", 2}, {"fluid", 2}, {"focuses", 2}, {"graphics", 2}, {"interesting", 2}, {"maximal", 2}, {"mechanics", 2}, {"order", 2}, {"outstanding", 2}, {"solutions", 2}, {"surface", 2}, {"tackle", 2}, {"techniques", 2}}|>, "1500423" -> <|"AwardTitle" -> "Turbulence Dynamics in the Presence of Flow Shear in a Collisional Plasma: Experiment-Model Cross-Validation", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "This project seeks to further our fundamental understanding of plasma turbulence and flows by making detailed comparisons of large-scale computer models with carefully controlled laboratory experiments. Turbulence and its effects are ubiquitous in magnetized plasmas on Earth, in near space, and throughout the universe. Turbulence can drive increased transport of particles, heat, and momentum, which affects our ability to confine plasmas for applications on Earth, such as fusion energy, and can play an important role in accelerating particles to high energies, for example in the space weather environment comprising the Sun and Earth. The large numbers of high energy particles generated during space weather events have the potential to seriously impact satellites, communications, and power systems on Earth. Being able to reliably predict such events requires a detailed understanding of the underlying physics, including the physics of turbulence and the interaction of turbulence and flows. \n\nThe goal of this work is to validate, through controlled laboratory experiments and close experiment-theory-model coupling, a fully global, nonlinear two-fluid model appropriate for understanding turbulence and transport dynamics in a collisional laboratory plasma. Despite a long and ongoing history of work to understand the dynamics of plasma turbulence in the presence of sheared flows, there still appears to be no validated model that can accurately reproduce experimental observations over a wide range of turbulent states in even relatively simple, well-controlled experiments. Even in these 'simple' laboratory experiments, enough complicating physics are present so that interpreting measurements purely experimentally, via quasilinear theories, or via local nonlinear models seems to be difficult or impossible. The proposed experiments will take place in the dual-source HelCat (Helicon-Cathode) device at the University of New Mexico. HelCat is a flexible device that provides unique capabilities important to these experiments. The GBS (Global Braginskii Solver), a fully 3D global drift-reduced Braginskii solver that has been used previously to model both linear and toroidal devices will be used to model these experiments. Experiment-model comparisons will be undertaken under a wide range of conditions, from coherent to fully-developed turbulent states.", "AwardID" -> "1500423", "Institution" -> Entity["NSFInstitution", "UniversityOfNewMexico"], "Investigators" -> {Entity["NSFInvestigator", "BarrettRogers"], Entity["NSFInvestigator", "MarkGilmore"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500423&HistoricalAwards=false"], "KeywordTally" -> {{"experiments", 7}, {"turbulence", 5}, {"Earth", 4}, {"laboratory", 4}, {"model", 4}, {"flows", 3}, {"particles", 3}, {"physics", 3}, {"plasma", 3}, {"space", 3}, {"understanding", 3}, {"Braginskii", 2}, {"comparisons", 2}, {"controlled", 2}, {"detailed", 2}, {"device", 2}, {"dynamics", 2}, {"energy", 2}, {"events", 2}, {"fully", 2}, {"global", 2}, {"HelCat", 2}, {"high", 2}, {"important", 2}, {"models", 2}, {"nonlinear", 2}, {"plasmas", 2}, {"range", 2}, {"simple", 2}, {"states", 2}, {"transport", 2}, {"Turbulence", 2}, {"turbulent", 2}, {"used", 2}, {"via", 2}, {"weather", 2}, {"wide", 2}, {"work", 2}}|>, "1500424" -> <|"AwardTitle" -> "Critical Nonlinear Dispersive Equations", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[112228, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This project will study dispersive partial differential equations. Such equations model many different phenomena, among them the propagation of various kinds of waves, such as water waves and laser light. These equations also model certain phenomena in particle physics. This project attempts to understand long-time behavior of such equations and related systems.\n\nThere are a number of problems that will be studied in the course of this endeavor. The study will mainly revolve around the three well-known dispersive partial differential equations: wave, Schrodinger, and Korteweg de Vries. A great deal is unknown for the focusing Schrodinger and Korteweg de Vries (KdV) problems, particularly for the mass-critical problem. The PI intends to study the focusing, mass-critical Schrodinger problem for mass above the mass of the ground state, as well as the focusing gKdV problem for large mass below the mass of the ground state. The PI also plans to extend recent work with the I-method to the wave and Klein-Gordon equations. Finally, the PI will study the ultra hyperbolic Schrodinger equation.", "AwardID" -> "1500424", "Institution" -> Entity["NSFInstitution", "JohnsHopkinsUniversity"], "Investigators" -> {Entity["NSFInvestigator", "BenjaminDodson"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500424&HistoricalAwards=false"], "KeywordTally" -> {{"equations", 6}, {"mass", 4}, {"Schrodinger", 4}, {"study", 4}, {"focusing", 3}, {"PI", 3}, {"problem", 3}, {"de", 2}, {"differential", 2}, {"dispersive", 2}, {"ground", 2}, {"Korteweg", 2}, {"mass-critical", 2}, {"model", 2}, {"partial", 2}, {"phenomena", 2}, {"problems", 2}, {"project", 2}, {"state", 2}, {"Vries", 2}, {"wave", 2}, {"waves", 2}}|>, "1500427" -> <|"AwardTitle" -> "Collaborative Research: Experimental and Theoretical Study of the Plasma Physics of Antihydrogen Generation and Trapping", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[228000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "The long-term goals of this research address the very basis of our understanding of the world around us. Potentially, it has deep implications on the nature of particle interactions, on the question of matter-antimatter symmetry, and on cosmology. At the same time, this research is uniquely visible because the study of antimatter is accessible and fascinating to the public. Antihydrogen experiments are sufficiently simple that they can be comprehended in their entirety by graduate students. Consequently, they offer students a broad education. Experimental students learn beam and plasma physics, experimental planning and design, instrumentation, electronics, cryogenics, magnetics and software development. Along with theory development, theory students can make critical contributions to the design, operation, and analysis of the experiments. The relative accessibility of the material makes it easy to integrate undergraduate students into both the experimental and theoretical program. The research includes significant participation by members of underrepresented groups.\n\nThe research is primarily focused on the immediate plasma and atomic physics issues surrounding improving the trapping of antihydrogen, and on the design of a third generation trap optimized for gravitational research. The physics issues will be studied with experiments at Berkeley and at CERN, with classical trajectory Monte Carlo, molecular dynamics, Vlasov codes and 3D Particle-In-Cell codes, and with analytic theory. Some of the questions that will be addressed include: achieving improved (lower) lepton and antiproton temperatures; studying how leptons interact with the background radiation field; studying how leptons interact with resonant cavities; improved plasma diagnostics; and improved mixing of positrons and antiprotons, so that more of the resultant antihydrogen can be held in a very shallow neutral trap. While the motivation for seeking answers to these questions comes from antihydrogen research, many of these questions raise novel and deep issues in plasma and atomic physics. This research is co-sponsored by the NSF's Physics Division and the Office of International Science and Engineering.", "AwardID" -> "1500427", "Institution" -> Entity["NSFInstitution", "UniversityOfNorthTexas"], "Investigators" -> {Entity["NSFInvestigator", "CarlosOrdonez"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500427&HistoricalAwards=false"], "KeywordTally" -> {{"research", 7}, {"students", 5}, {"physics", 4}, {"plasma", 4}, {"antihydrogen", 3}, {"design", 3}, {"experiments", 3}, {"improved", 3}, {"issues", 3}, {"questions", 3}, {"theory", 3}, {"atomic", 2}, {"codes", 2}, {"deep", 2}, {"development", 2}, {"experimental", 2}, {"interact", 2}, {"leptons", 2}, {"studying", 2}, {"trap", 2}}|>, "1500438" -> <|"AwardTitle" -> "Regularity Problems in the Calculus of Variations and Elliptic Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[149761, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This project focuses on central problems in classical fields such as the calculus of variations and free boundary problems. Some problems find their motivation in the applied sciences and therefore offer opportunities for collaborations among mathematicians and other researchers. For example, the so-called \"one-phase problem\" describes the motion of a fluid in which a cavity is present that is a mixture of vapor and gas and the pressure on the cavity is constant. Other problems under investigation are related to issues of optimal transportation and allocation of resources. All such problems require the development of new sophisticated techniques, and progress will be disseminated to the scientific community to invigorate the advancement of the theory.\n\nThe PI will study the classification of cones in low dimensions for the \"one-phase\" free boundary problem. As a tool in the analysis of free boundaries, the PI will investigate some boundary Harnack type results. In the context of optimal transportation, the PI is interested in the higher regularity for a class of degenerate Monge-Ampere equations in which the right hand side vanishes on the boundary. Finally, parts of this project deal with the fundamental question of local regularity of minimizers in the calculus of variations. In particular, in the scalar case the PI will investigate situations in which the integrand becomes highly degenerate on some compact set. In the vectorial case, the PI plans to construct some interesting singular minimizers in low dimensions and will also explore a viscosity approach to regularity for certain types of functionals.", "AwardID" -> "1500438", "Institution" -> Entity["NSFInstitution", "ColumbiaUniversity"], "Investigators" -> {Entity["NSFInvestigator", "OvidiuSavin"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500438&HistoricalAwards=false"], "KeywordTally" -> {{"PI", 5}, {"problems", 5}, {"boundary", 4}, {"free", 3}, {"regularity", 3}, {"calculus", 2}, {"case", 2}, {"cavity", 2}, {"degenerate", 2}, {"dimensions", 2}, {"investigate", 2}, {"low", 2}, {"minimizers", 2}, {"optimal", 2}, {"-phase", 2}, {"problem", 2}, {"project", 2}, {"transportation", 2}, {"variations", 2}}|>, "1500439" -> <|"AwardTitle" -> "Collaborative Research: Heating the Solar Chromosphere Through Plasma Turbulence", "AwardEffectiveDate" -> DateObject[{2015, 7, 15}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[175000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "The goal of this project is to provide a detailed verifiable explanation of the origin of the heating of the solar atmosphere. Most of the light reaching Earth originates at the 'surface' of the sun, a region called the photosphere. However, the regions of the solar atmosphere immediately above this surface, the solar chromosphere and corona, create most of the dangerous Ultraviolet (UV) and X-ray radiation. These regions also generate the solar wind, a stream of charged particles that pass the Earth at speeds in excess of 400km/s. Both the rapidly changing radiation and the solar wind create hazards for spacecraft, astronauts, and have a number of important terrestrial impacts. A long-standing mystery has prevented scientists from understanding and accurately modeling the chromosphere and corona. A short distance above the 'surface' of the sun, the solar atmosphere's temperature jumps up by a factor of two to three. The goal of this project is to provide an explanation of the origin of this heating. The project will also provide opportunities to recruit and train student researchers in plasma and solar physics, simulations, and modeling at the Boston University. Many of the Boston University PI's undergraduate research advisees, about half of whom are women, have continued on to graduate school. \n\nThis research will examine whether solar plasma flows emerging from the photosphere can transfer sufficient energy into turbulent plasma of the solar atmosphere, which, in turn, will heat the chromosphere sufficiently to explain whether the observed UV spectra originate there. It will also evaluate whether this mechanism can account for chromospheric spectral observations. This requires four linked research tasks: (1) solving for plasma drifts and fields when a convecting neutral gas pushes it across magnetic field lines; (2) analyzing the theory of streaming instabilities applicable to the collisional plasma found there; (3) performing a series of kinetic simulations to explore the nonlinear and thermal properties of the resulting turbulence; and (4) incorporating the resulting electron heating into a radiative transport code in order to evaluate its impact on chromospheric radiance. This research combines several research areas encompassed by the NSF/DOE Partnership in Basic Science and Engineering.", "AwardID" -> "1500439", "Institution" -> Entity["NSFInstitution", "TrusteesOfBostonUniversity"], "Investigators" -> {Entity["NSFInvestigator", "YakovDimant"], Entity["NSFInvestigator", "MeersOppenheim"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500439&HistoricalAwards=false"], "KeywordTally" -> {{"solar", 9}, {"plasma", 5}, {"research", 5}, {"atmosphere", 3}, {"chromosphere", 3}, {"heating", 3}, {"project", 3}, {"provide", 3}, {"surface", 3}, {"Boston", 2}, {"chromospheric", 2}, {"corona", 2}, {"create", 2}, {"Earth", 2}, {"evaluate", 2}, {"explanation", 2}, {"goal", 2}, {"modeling", 2}, {"origin", 2}, {"photosphere", 2}, {"radiation", 2}, {"regions", 2}, {"resulting", 2}, {"simulations", 2}, {"sun", 2}, {"University", 2}, {"UV", 2}, {"wind", 2}}|>, "1500440" -> <|"AwardTitle" -> "Potential Theory of Functions of Bounded Variation and Quasiconformal Maps", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[185525, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "When we view images of objects, what we see are various locations of the object emitting different intensities of light. We can think of the image of the object as formed by a collection of surfaces of different shapes, each with its own uniform brightness. Similarly, in the study of various mathematical objects such as functions that measure temperature at different locations, functions that measure electro-magnetic intensities, and functions that measure the velocity of fluid particles at various places in a fluid, can be understood in terms of the shape of the level sets of the function. (A level set is a set where the function takes on a given constant value.) This project in metric space analysis explores the behavior of functions that arise in the study of potential theory and quasiconformal mappings in terms of level sets. Applications of the the research project include image processing and edge detection. Many components of this project are suitable dissertation material for graduate students, and therefore will contribute to the training of future members of the STEM workforce.\n\nThis project is concerned with links between geometry of a metric space given in terms of its sets of finite perimeter on the one hand, and nonlinear potential theory and quasiconformal mappings on the other hand. The spaces considered are equipped with a doubling measure supporting a 1-Poincare inequality. In the first part of the project the PI will explore interactions between collections of sets of finite perimeter and quasiconformal mappings, and between collections of sets of finite perimeter and nonlinear potential theory. The second part of the project will explore \"tangent space\" regularity of sets of quasiminimal boundary surfaces. The third part of the project is to develop a potential theory for functions of bounded variation. The last part of the project is to obtain a characterization of certain Poincare inequalities in terms of modulus of families of sets of finite perimeter. Applications of the research include further understanding of connections between metric geometry related to sets of finite perimeter and solutions to certain nonlinear partial differential equations. Such sets arise in the study of image processing and edge detection, while abstract metric spaces arise in Riemannian manifolds theory when considering Gromov-Hausdorff limit spaces as found in the works of Cheeger, Gromov, and Perelman. Furthermore, these projects will expand the current knowledge about geometry and the theory of sets of finite perimeter in Carnot-Caratheodory spaces.", "AwardID" -> "1500440", "Institution" -> Entity["NSFInstitution", "UniversityOfCincinnatiMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "NageswariShanmugalingam"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500440&HistoricalAwards=false"], "KeywordTally" -> {{"sets", 10}, {"project", 8}, {"finite", 6}, {"perimeter", 6}, {"theory", 6}, {"functions", 5}, {"measure", 4}, {"metric", 4}, {"potential", 4}, {"spaces", 4}, {"terms", 4}, {"arise", 3}, {"different", 3}, {"geometry", 3}, {"image", 3}, {"level", 3}, {"mappings", 3}, {"nonlinear", 3}, {"quasiconformal", 3}, {"space", 3}, {"study", 3}, {"various", 3}, {"Applications", 2}, {"certain", 2}, {"collections", 2}, {"detection", 2}, {"edge", 2}, {"explore", 2}, {"fluid", 2}, {"function", 2}, {"given", 2}, {"hand", 2}, {"include", 2}, {"intensities", 2}, {"locations", 2}, {"object", 2}, {"objects", 2}, {"processing", 2}, {"research", 2}, {"set", 2}, {"surfaces", 2}}|>, "1500448" -> <|"AwardTitle" -> "Doctoral Dissertation Research: Testing for Ecological Speciation with Phylogeographic Data", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2016, 5, 31}], "AwardAmount" -> Quantity[16226, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010206", "ProgramOfficer" -> "Simon Malcomber", "Abstract" -> "The various processes involved in the formation of species are not well understood. One of the leading hypotheses, ecological speciation, proposes that populations of the same species living in different regions will diverge over time in response to differing environments. Eventually these changes will accumulate, resulting in the formation of different species. This research will test the hypothesis of ecological speciation by studying multiple species of snakes in the Sonoran and Chihuahuan deserts where it has been shown that closely populations in the two regions have divergent DNA sequences. Using a combination of genomic DNA sequence data, anatomy, morphology, and climate data, researchers will test whether predictions from ecological speciation account for differences observed between these recently diverged populations. This research will train one graduate student and provide undergraduate students with early training in molecular evolutionary studies and diverse laboratory techniques. Data collected from the research will be used to design a new course for graduate students, who can then apply similar methods to address their own research questions in systematics and evolutionary biology.\n\nThe ecological speciation hypothesis states that reproductive isolation is a byproduct of natural selection on divergent ecologies between species. Alternatively there are several non-ecological mechanisms by which speciation can occur, including genetic drift, the fixation of incompatible mutations, or sexual selection. Under the hypothesis of ecological speciation it is expected that reproductive isolation will be correlated with ecological differentiation. The proposed study will test for the signature of ecological speciation in a group of snakes that share a common phylogeographic break between the Sonoran and Chihuahuan deserts. Researchers will collect high-throughput genomic DNA sequence data and measure reproductive isolation between pairs of sister taxa. Ecological niche models and morphometrics will be used to measure ecological divergence between populations. Bayesian model averaging will then be used to assess the affects of ecological divergence and time on reproductive isolation. This research will address whether ecological divergence is driving speciation at recent time scales, and test its importance in generating species level diversity. Further, the study will help to illuminate the mechanisms responsible for generating high regional species diversity in this biodiversity hotspot.", "AwardID" -> "1500448", "Institution" -> Entity["NSFInstitution", "CUNYGraduateSchoolUniversityCenter"], "Investigators" -> {Entity["NSFInvestigator", "FrankBurbrink"], Entity["NSFInvestigator", "EdwardMyers"]}, "ProgramElements" -> {{"Code" -> "1171", "Text" -> "PHYLOGENETIC SYSTEMATICS"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500448&HistoricalAwards=false"], "KeywordTally" -> {{"ecological", 10}, {"speciation", 8}, {"species", 7}, {"research", 5}, {"isolation", 4}, {"populations", 4}, {"reproductive", 4}, {"test", 4}, {"data", 3}, {"divergence", 3}, {"DNA", 3}, {"hypothesis", 3}, {"time", 3}, {"used", 3}, {"address", 2}, {"Chihuahuan", 2}, {"deserts", 2}, {"different", 2}, {"divergent", 2}, {"diversity", 2}, {"evolutionary", 2}, {"formation", 2}, {"generating", 2}, {"genomic", 2}, {"graduate", 2}, {"measure", 2}, {"mechanisms", 2}, {"regions", 2}, {"selection", 2}, {"sequence", 2}, {"snakes", 2}, {"Sonoran", 2}, {"students", 2}, {"study", 2}}|>, "1500449" -> <|"AwardTitle" -> "Endpoint Behavior of Modulation Invariant Singular Integrals", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[151237, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Harmonic analysis studies how signals (functions) break up into a superposition of basic harmonics--signals with a well-specified duration, intensity and frequency--and how operations (filtering) applied to these components affect the reconstructed signal. Variants of this time-frequency decomposition process are performed in countless real-world applications, such as audio or image compression and filtering, image pattern recognition, data assimilation and denoising. One of the broad objectives of this project is the investigation of the theoretical feasibility threshold of the time-frequency techniques in terms of the relative size and smoothness of the input. An analogous procedure is adopted in tomographic imaging, where a solid body is reconstructed by means of sampling its density along penetrating waves, mathematically described as lines in three-dimensional space. This project will study mathematical toy models of sampling along lines or curves, whose theoretical understanding may play a significant role in the derivation of improved analytical image reconstruction methods. An integral component of the project is the training of graduate and undergraduate students within the active research group in harmonic analysis at Brown University, with the particular intent of attracting young and promising researchers to the field.\n\nThe central objects of study of this project are modulation-invariant singular integrals and their behavior at or near the boundary of their known boundedness range. The model question, involving Carleson's maximal partial Fourier sum operator, is the characterization of the sharp integrability order sufficient for the almost-everywhere pointwise convergence of the Fourier series of a periodic function. The second, deeply related question concerns the extension of the Lacey-Thiele Holder-type estimates for the bilinear Hilbert transform to the boundary of the known range. Together with his collaborators, the principal investigator has recently obtained the current best results for both problems, relying in particular on a newly developed Calderon-Zygmund decomposition adapted to the modulation-invariant setting. It is expected that further developments of this technique will lead to additional improvements towards the solution of these two central questions, as well as of other significant open problems. A standout question is the extension of the known uniform estimates for the bilinear Hilbert transform to the full expected range of exponents, completing the original program of Calderon for the boundedness of the first commutator. Another central direction of the proposed investigation is the study of singular integral operators with rotational symmetries, a prime example of which is the Hilbert transform along a smooth vector field in the plane, by means of multiparameter time-frequency analysis techniques. Further improvements of the aforementioned techniques are also expected to impact on several questions concerning summability of multiple Fourier series.", "AwardID" -> "1500449", "Institution" -> Entity["NSFInstitution", "BrownUniversity"], "Investigators" -> {Entity["NSFInvestigator", "FrancescoDiPlinio"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500449&HistoricalAwards=false"], "KeywordTally" -> {{"project", 4}, {"analysis", 3}, {"central", 3}, {"expected", 3}, {"Fourier", 3}, {"Hilbert", 3}, {"image", 3}, {"known", 3}, {"question", 3}, {"range", 3}, {"study", 3}, {"techniques", 3}, {"time-frequency", 3}, {"transform", 3}, {"bilinear", 2}, {"boundary", 2}, {"boundedness", 2}, {"decomposition", 2}, {"estimates", 2}, {"extension", 2}, {"filtering", 2}, {"improvements", 2}, {"integral", 2}, {"investigation", 2}, {"lines", 2}, {"means", 2}, {"modulation-invariant", 2}, {"particular", 2}, {"problems", 2}, {"questions", 2}, {"reconstructed", 2}, {"sampling", 2}, {"series", 2}, {"signals", 2}, {"significant", 2}, {"singular", 2}, {"theoretical", 2}}|>, "1500454" -> <|"AwardTitle" -> "Modern Aspects of Complex Geometry", "AwardEffectiveDate" -> DateObject[{2015, 3, 1}], "AwardExpirationDate" -> DateObject[{2017, 2, 28}], "AwardAmount" -> Quantity[49935, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This award provides funding to help defray the expenses of participants in the conference \"Modern Aspects of Complex Geometry,\" held May 14-17, 2015, on the campus of the University of Cincinnati. Conference web site: www.artsci.uc.edu/departments/math/complex_geometry_conference.html\n\nThis is a conference in the general area of geometric function theory. The event seeks to focus attention on and highlight connections between a variety of topics, including the theory of quasiconformal mappings, mappings of finite distortion, potential theory, analysis on metric spaces, and Teichmuller theory. The conference program provides ample opportunity for graduate students, postdocs, and other young scientists to present their work.", "AwardID" -> "1500454", "Institution" -> Entity["NSFInstitution", "UniversityOfCincinnatiMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "DavidHerron"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500454&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 4}, {"conference", 3}, {"mappings", 2}, {"provides", 2}}|>, "1500455" -> <|"AwardTitle" -> "2015-2017 SUNY LSAMP Bridge to the Doctorate at Binghamton University", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2017, 7, 31}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Martha L. James", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the STEM workforce through their efforts at significantly increasing the numbers of students from historically underrepresented minority populations to successfully complete high quality degree programs in science, technology, engineering and mathematics (STEM) disciplines. The LSAMP Bridge to the Doctorate (LSAMP-BD) activity provides two-year support at the postbaccalaurate level for students from historically underrepresented minority populations to matriculate in STEM graduate programs with the ultimate goal of earning a doctoral degree in a STEM discipline. Participants are selected from LSAMP institutions nationwide. The State University of New York System Louis Stokes Alliance for Minority Participation (SUNY LSAMP) under the leadership of Stony Brook University has chosen Binghamton University as the host site for the 2015-2017 BD program in which a cohort of twelve LSAMP certified students selected from the national pool will engage in STEM research, academics and professional development activities leading to STEM Master's and Doctoral degree completion. The BD program at Binghamton University provides a comprehensive set of support services that monitors student progress, builds a strong BD community, and increases BD students' academic and professional skills. \n\nNine cohorts of students have matriculated in SUNY LSAMP graduate LSAMP-BD programs at Stony Brook, Buffalo, Binghamton and Albany since 2006. The programs promote systemic change in graduate education practices and policy in ways that increase the success of individual students on the doctoral pathway and the effectiveness of STEM graduate programs, continuing the goal of diversifying America's STEM workforce. The program at Binghamton University will be externally evaluated and students will be tracked throughout the program and into STEM careers following completion of STEM doctoral degree programs. Collaborations with other STEM networks and resources internal and external to the state as well as other graduate programs, such as NSF's Graduate Research Fellowship Program (GRFP), Alliances for Graduate Education and the Professoriate (AGEP) and institutional resources will further ensure that students complete the STEM terminal degree.", "AwardID" -> "1500455", "Institution" -> Entity["NSFInstitution", "SUNYAtStonyBrook"], "Investigators" -> {Entity["NSFInvestigator", "DavidFerguson"], Entity["NSFInvestigator", "ShaniseKent"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500455&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 12}, {"students", 8}, {"programs", 7}, {"LSAMP", 6}, {"degree", 5}, {"graduate", 5}, {"program", 5}, {"University", 5}, {"BD", 4}, {"Binghamton", 4}, {"doctoral", 3}, {"Alliances", 2}, {"Brook", 2}, {"complete", 2}, {"completion", 2}, {"diversifying", 2}, {"goal", 2}, {"Graduate", 2}, {"historically", 2}, {"Louis", 2}, {"LSAMP-BD", 2}, {"minority", 2}, {"Minority", 2}, {"Participation", 2}, {"populations", 2}, {"professional", 2}, {"provides", 2}, {"resources", 2}, {"selected", 2}, {"Stokes", 2}, {"Stony", 2}, {"SUNY", 2}, {"support", 2}, {"underrepresented", 2}, {"workforce", 2}}|>, "1500460" -> <|"AwardTitle" -> "Particle Acceleration During Collisionless Magnetic Reconnection", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[170000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "This project is focused on the understanding of particle acceleration during the process of magnetic reconnection. Magnetic reconnection is a fundamental process in which magnetic energy is converted into high-speed flows and energetic particles. It underlies important phenomena in nature, including solar flares, strong disturbances in the Earth's magnetic field, and disruptions in laboratory fusion experiments. Magnetic reconnection is also the driver of space weather, which can negatively impact satellite communications and threaten astronauts in space. Great progress has been made on understanding the mechanisms for the fast release of magnetic energy seen in nature and the laboratory during magnetic reconnection. Solar observations suggest that a large fraction of the magnetic energy released appears in the form of energetic particles. The mechanisms for particle acceleration are not understood and are the focus of this research project. The project will include active involvement of undergraduate students, the training of graduate students, including female graduate students, and thus further the broad educational goals of NSF.\n\nThe technical goal of this research program is to understand electron and ion heating and acceleration during magnetic reconnection and to develop a model for particle acceleration that can be compared with observations. Particle-in-cell simulations and analytic approaches will be used to address four key issues related to electron and ion acceleration during magnetic reconnection: to identify and quantify the dominant mechanisms for electron acceleration; to establish the physics basis for the ubiquitous observations of power-law spectra of energetic particles; to establish the mechanism for ion acceleration and abundance enhancements in impulsive flares; and to develop a Fokker-Planck model of particle acceleration that can be used to predict the hazards associated with space weather. Collaborations will be continued with scientists working on laboratory experiments and with satellite data to benchmark the theoretical predictions with observations.", "AwardID" -> "1500460", "Institution" -> Entity["NSFInstitution", "UniversityOfMarylandCollegePark"], "Investigators" -> {Entity["NSFInvestigator", "JamesDrake"], Entity["NSFInvestigator", "MichaelSwisdak"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500460&HistoricalAwards=false"], "KeywordTally" -> {{"acceleration", 8}, {"magnetic", 8}, {"reconnection", 6}, {"observations", 4}, {"particle", 4}, {"electron", 3}, {"energetic", 3}, {"energy", 3}, {"ion", 3}, {"laboratory", 3}, {"mechanisms", 3}, {"particles", 3}, {"project", 3}, {"space", 3}, {"students", 3}, {"develop", 2}, {"establish", 2}, {"experiments", 2}, {"flares", 2}, {"graduate", 2}, {"including", 2}, {"Magnetic", 2}, {"model", 2}, {"nature", 2}, {"process", 2}, {"research", 2}, {"satellite", 2}, {"understanding", 2}, {"used", 2}, {"weather", 2}}|>, "1500461" -> <|"AwardTitle" -> "Decouplings and applications", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[147755, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The principal investigator, in collaboration with Jean Bourgain, has recently created a new set of tools that can successfully address a wide range of problems in the fields of number theory and partial differential equations. Until recently, many of these problems seemed unrelated. In light of his work with Bourgain, these problems are now understood as part of a more general theory that the two call \"decoupling.\" The methods pertain to the field of modern harmonic analysis, a natural framework that allows for the formulation of a general enough theory. This project seeks to enlarge the range of applicability of decouplings, with some high-value targets in sight. A surprising feature of the research is that it removes certain restrictions on frequencies that were thought to be necessary in earlier work. In particular, the old requirement that frequencies have integer coordinates is replaced with the weaker assumption that sufficient spatial separation exists between frequencies. It is expected that the tools that will be developed will be accessible and useful to a large part of the mathematical community.\n\nDecouplings are certain generalizations of the Littlewood--Paley theory in the presence of curvature. The principal investigator's progress in pursuing the line of research related to this subject has relied hitherto on the interplay between multilinear and linear multiscale analysis. He has successfully addressed the case when the relevant manifold is a hypersurface with nonzero Gaussian curvature. He now proposes to develop the optimal decoupling theory for nondegenerate curves. Such a theory has the potential to achieve almost unprecedented applications of harmonic analysis to number theory. One notable example is the resolution of Vinogradov's mean value theorem. There is an interesting related circle of problems for the cone. The fact that it has zero Gaussian curvature poses a new level of difficulty that will most certainly require new ideas. Understanding the cone is part of a more ambitious project that will aim at understanding the decoupling theory for real analytic surfaces. There are further important related questions that remain to be explored, in connection with various restriction theorems and the Kakeya conjectures.", "AwardID" -> "1500461", "Institution" -> Entity["NSFInstitution", "IndianaUniversity"], "Investigators" -> {Entity["NSFInvestigator", "CiprianDemeter"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500461&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 8}, {"problems", 4}, {"analysis", 3}, {"curvature", 3}, {"decoupling", 3}, {"frequencies", 3}, {"new", 3}, {"related", 3}, {"Bourgain", 2}, {"certain", 2}, {"cone", 2}, {"Gaussian", 2}, {"general", 2}, {"harmonic", 2}, {"number", 2}, {"principal", 2}, {"project", 2}, {"range", 2}, {"recently", 2}, {"research", 2}, {"successfully", 2}, {"tools", 2}, {"work", 2}}|>, "1500468" -> <|"AwardTitle" -> "Quantitative and Qualitative properties of solutions of partial differential equations", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[128916, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The proposal is concerned with the analysis and applications of nonlinear partial differential equations. The model problems in this proposal arise from the study of various nonlinear phenomena and other scientific disciplines, including condensed matter physics, elasticity, inverse problem, electrodynamics, quantum mechanics, fluid mechanics, mathematics biology, differential geometry, etc. The focus of the proposal research is the investigation of the quantitative and qualitative properties of solutions for partial differential equations. Providing quantitative and qualitative information for the solutions is fundamental and essential in the study of partial differential equations, which lies in the core of mathematical analysis. It is often the case that the most effective and economical way in scientific research is to explore properties of solutions and then to develop algorithm in accordance. Besides being very useful in applied science, the investigation of various kinds of structures and properties of solutions for various types of equations absolutely leads to new theories in mathematics.\n\nThe proposed projects include quantitative uniqueness, eigenfunction and eigenvalue estimates, as well as Liouville-type theorems. Techniques and ideas from analysis area, such as elliptic estimates and Fourier analysis, will be combined and applied into this project. The proposed research should enhance the understanding of classical and Steklov eigenvalue problems, semilinear and higher order elliptic equations, wave equations, fractional Laplacians, fully nonlinear equations, etc. Further research will be devoted to the study of quantitative uniqueness of parabolic differential equations and other important equations from mathematical physics. Another related direction is the study of phase separations phenomenon in Bose-Einstein condensate. Emphasis will be placed on the two components Gross-Pitaevskki system. An important part of proposed research is on eigenfunction and eigenvalue estimates. Techniques and insights in the various areas cross-fertilize each other in a fruitful way in this area. The topics consist of measure of nodal sets (zero level sets), asymptotic behavior of eigenvalues, Lebesgue norm estimates, as well as doubling estimates of Steklov eigenfunctions and classical eigenfunctions. Much effort will be made towards Yau's conjecture asserting that the size of nodal sets is comparable to its frequency. The principal investigator will also continue the previous investigation on Liouville-type theorems on nonexistence of solutions for fractional Laplacian equations and fully nonlinear partial differential equations.", "AwardID" -> "1500468", "Institution" -> Entity["NSFInstitution", "JohnsHopkinsUniversity"], "Investigators" -> {Entity["NSFInvestigator", "JiuyiZhu"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500468&HistoricalAwards=false"], "KeywordTally" -> {{"equations", 11}, {"differential", 6}, {"estimates", 5}, {"research", 5}, {"solutions", 5}, {"analysis", 4}, {"nonlinear", 4}, {"partial", 4}, {"quantitative", 4}, {"study", 4}, {"various", 4}, {"eigenvalue", 3}, {"investigation", 3}, {"properties", 3}, {"proposal", 3}, {"proposed", 3}, {"sets", 3}, {"applied", 2}, {"area", 2}, {"classical", 2}, {"eigenfunction", 2}, {"eigenfunctions", 2}, {"elliptic", 2}, {"etc", 2}, {"fractional", 2}, {"fully", 2}, {"important", 2}, {"Liouville-type", 2}, {"mathematical", 2}, {"mechanics", 2}, {"nodal", 2}, {"physics", 2}, {"problems", 2}, {"qualitative", 2}, {"scientific", 2}, {"Steklov", 2}, {"Techniques", 2}, {"theorems", 2}, {"uniqueness", 2}, {"way", 2}}|>, "1500470" -> <|"AwardTitle" -> "Collaborative Research: Experimental and Theoretical Study of the Plasma Physics of Antihydrogen Generation and Trapping", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[15000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "The long-term goals of this research address the very basis of our understanding of the world around us. Potentially, it has deep implications on the nature of particle interactions, on the question of matter-antimatter symmetry, and on cosmology. At the same time, this research is uniquely visible because the study of antimatter is accessible and fascinating to the public. Antihydrogen experiments are sufficiently simple that they can be comprehended in their entirety by graduate students. Consequently, they offer students a broad education. Experimental students learn beam and plasma physics, experimental planning and design, instrumentation, electronics, cryogenics, magnetics and software development. Along with theory development, theory students can make critical contributions to the design, operation, and analysis of the experiments. The relative accessibility of the material makes it easy to integrate undergraduate students into both the experimental and theoretical program. The research includes significant participation by members of underrepresented groups.\n\nThe research is primarily focused on the immediate plasma and atomic physics issues surrounding improving the trapping of antihydrogen, and on the design of a third generation trap optimized for gravitational research. The physics issues will be studied with experiments at Berkeley and at CERN, with classical trajectory Monte Carlo, molecular dynamics, Vlasov codes and 3D Particle-In-Cell codes, and with analytic theory. Some of the questions that will be addressed include: achieving improved (lower) lepton and antiproton temperatures; studying how leptons interact with the background radiation field; studying how leptons interact with resonant cavities; improved plasma diagnostics; and improved mixing of positrons and antiprotons, so that more of the resultant antihydrogen can be held in a very shallow neutral trap. While the motivation for seeking answers to these questions comes from antihydrogen research, many of these questions raise novel and deep issues in plasma and atomic physics. This research is co-sponsored by the NSF's Physics Division and the Office of International Science and Engineering.", "AwardID" -> "1500470", "Institution" -> Entity["NSFInstitution", "PurdueUniversity"], "Investigators" -> {Entity["NSFInvestigator", "FrancisRobicheaux"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500470&HistoricalAwards=false"], "KeywordTally" -> {{"research", 7}, {"students", 5}, {"physics", 4}, {"plasma", 4}, {"antihydrogen", 3}, {"design", 3}, {"experiments", 3}, {"improved", 3}, {"issues", 3}, {"questions", 3}, {"theory", 3}, {"atomic", 2}, {"codes", 2}, {"deep", 2}, {"development", 2}, {"experimental", 2}, {"interact", 2}, {"leptons", 2}, {"studying", 2}, {"trap", 2}}|>, "1500481" -> <|"AwardTitle" -> "Career Advancement for Women Through Research-Focused Networks", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2020, 8, 31}], "AwardAmount" -> Quantity[749984, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "dana britton", "Abstract" -> "This project by the Association of Women in Mathematics (AWM) focuses on fostering research collaborations and establishing research networks for women mathematicians in the early to mid-stages of their careers. Research collaborations have become an increasingly essential part of a successful career in mathematics. In theoretical sciences, unlike laboratory sciences, there is no structure in which collaborations and mentor relationships naturally arise. It is thus critical that women, beginning early in their career, attend research conferences in their area of specialization, interact productively with other participants, and have access to research-based networks. To facilitate such networks, AWM plans to organize a series of conferences and workshops aimed at fostering research collaborations and building sustainable networks. These networks will be established at Research Collaboration Conferences for Women (RCCWs), which are week-long conferences, held at mathematics institutes, where junior and senior women come together to work on pre-defined research problems. AWM will expand the number and scope of the RCCWs and organize a series of follow-up events to help sustain and grow the resulting networks. Expected outcomes of this project include more invitations to speak at conferences, more collaborative research, a higher level of productivity for the women involved, and decreased attrition. The networks created by this project will not be static and will welcome new researchers as they enter the field. \n\nStudies conducted through this project will focus on understanding the effectiveness of research collaboration networks in helping to advance women's research careers to the highest levels of the profession. By promoting research collaborations and forming networks of women with related research interests, the proposed workshops will help both senior and junior women increase their visibility in and contributions to the research community. This project will also add to our understanding of the impact of networks and mentor relationships based on shared research interests in addition to shared demographic characteristics. The research and interactive seminars designed for this project have the potential to become models for future events of this kind and for other theoretical sciences. \n\nThe NSF ADVANCE Partnerships for Learning and Adaptation Networks (PLAN) program track supports projects that promote the adaptation and implementation of previously effective ADVANCE programs in new contexts and the testing of innovative strategies to promote the participation, success, and advancement of women in STEM academic careers. PLAN projects also contribute to the knowledge base on gender equity in STEM academic careers.", "AwardID" -> "1500481", "Institution" -> Entity["NSFInstitution", "AssociationForWomenInMathematics"], "Investigators" -> {Entity["NSFInvestigator", "RuthCharney"], Entity["NSFInvestigator", "MagnhildLien"], Entity["NSFInvestigator", "KristinLauter"]}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500481&HistoricalAwards=false"], "KeywordTally" -> {{"research", 13}, {"networks", 10}, {"women", 7}, {"project", 6}, {"collaborations", 5}, {"careers", 4}, {"conferences", 4}, {"AWM", 3}, {"sciences", 3}, {"academic", 2}, {"ADVANCE", 2}, {"career", 2}, {"early", 2}, {"events", 2}, {"fostering", 2}, {"help", 2}, {"interests", 2}, {"junior", 2}, {"mathematics", 2}, {"mentor", 2}, {"new", 2}, {"organize", 2}, {"PLAN", 2}, {"projects", 2}, {"promote", 2}, {"RCCWs", 2}, {"relationships", 2}, {"Research", 2}, {"senior", 2}, {"series", 2}, {"shared", 2}, {"STEM", 2}, {"theoretical", 2}, {"understanding", 2}, {"Women", 2}, {"workshops", 2}}|>, "1500484" -> <|"AwardTitle" -> "2015-2017 Louis Stokes Louisiana Bridge to the Doctorate - LSU BD-7: 2015 Cohort LA-BRIDGE", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2017, 7, 31}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Dr. A. James Hicks", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the STEM workforce through their efforts at significantly increasing the numbers of students from historically underrepresented minority populations to successfully complete high quality degree programs in science, technology, engineering and mathematics (STEM) disciplines. The LSAMP Bridge to the Doctorate (LSAMP BD) activity provides two-year support at the post-baccalaureate level for students from historically underrepresented minority populations to matriculate in STEM graduate programs with the ultimate goal of earning a doctoral degree in a STEM discipline. Participants are selected from LSAMP institutions nationwide. \n\nThe Louis Stokes Louisiana Alliance for Minority Participation (LS-LAMP), under the leadership of the Louisiana Board of Regents and Southern University, has chosen Louisiana State University (LSU) as the site for the seventh cohort of LSAMP Bridge to the Doctorate \nparticipants during 2015-2017. This cohort of twelve LSAMP BD students will engage in STEM research, academics and professional development leading to acceptance and completion of the doctoral program. The LS-LAMP graduate BD program at LSU has the potential to promote systemic change in graduate education practices and policy in ways that will increase the success of individual students on the doctoral pathway and the effectiveness of STEM graduate programs with a goal of diversifying America's STEM workforce.\n\nThe BD program at LSU employs a proven program of systemic mentoring with components for innovative recruitment, engagement, retention, evaluation, student tracking and dissemination. The program includes collaborations and linkages with other STEM networks and resources, such as the Louisiana Experimental Program to Stimulate Competitive Research (Louisiana EPSCoR), other state fellowship\nprograms as well as institutional resources to ensure students successful completion of the STEM doctoral degree. The program will be\nexternally evaluated and students will be tracked throughout the program and into\nSTEM careers following completion of STEM doctoral degree programs.", "AwardID" -> "1500484", "Institution" -> Entity["NSFInstitution", "LouisianaBoardOfRegents"], "Investigators" -> {Entity["NSFInvestigator", "IsiahWarner"], Entity["NSFInvestigator", "DiolaBagayoko"], Entity["NSFInvestigator", "KerryDavidson"], Entity["NSFInvestigator", "GuoqiangLi"], Entity["NSFInvestigator", "GloriaThomas"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500484&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 10}, {"program", 8}, {"LSAMP", 6}, {"students", 6}, {"doctoral", 5}, {"Louisiana", 5}, {"BD", 4}, {"degree", 4}, {"graduate", 4}, {"programs", 4}, {"completion", 3}, {"LSU", 3}, {"Bridge", 2}, {"cohort", 2}, {"diversifying", 2}, {"Doctorate", 2}, {"goal", 2}, {"historically", 2}, {"Louis", 2}, {"LS-LAMP", 2}, {"minority", 2}, {"Minority", 2}, {"Participation", 2}, {"populations", 2}, {"resources", 2}, {"Stokes", 2}, {"systemic", 2}, {"underrepresented", 2}, {"University", 2}}|>, "1500487" -> <|"AwardTitle" -> "CAREER: Parallel Dynamic Meshing Techniques for Simulation-Assisted Medical Interventions", "AwardEffectiveDate" -> DateObject[{2014, 10, 1}], "AwardExpirationDate" -> DateObject[{2017, 1, 31}], "AwardAmount" -> Quantity[272343, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "05090000", "ProgramOfficer" -> "Daniel Katz", "Abstract" -> "The investigators will research and develop parallel dynamic meshing algorithms, theory, and software for use in the patient-specific design of inferior vena cava (IVC) filters for improved treatment of deep vein thrombosis (DVT). This life-threatening disease results when blood clots form in a deep vein; DVT effects over 2,000,000 people in the U.S. each year. A mechanical filter is often placed in the IVC in order to trap a moving blood clot before it reaches the heart. A typical doctor uses only one or two types of filters when treating his patients rather than selecting the most appropriate IVC filter for his patient's condition. Current computational simulations of blood clot entrapment by IVC filters are of low accuracy. Hence, techniques to generate accurate meshes of the IVC and surrounding veins, IVC filter, and blood clots for use in such simulations will be developed. \n\nThe investigators will develop novel, parallel dynamic meshing techniques to generate accurate meshes of the IVC and surrounding veins, IVC filter, and blood clots. The investigators will develop parallel mesh warping algorithms and muticore software for updating the meshes in response to patient-specific deformations. Parallel geometric and topological mesh optimization methods in order to improve the quality of the meshes will be developed. The algorithms will be encapsulated in the form of a parallel dynamic meshing toolkit for simulation-assisted medical interventions. In addition, the researchers will develop a theoretical framework for dynamic meshing for improved quantitative understanding of deformations. Educational activities at the college- and pre-college level will be designed to build pathways for women and underrepresented students to pursue computational science.", "AwardID" -> "1500487", "Institution" -> Entity["NSFInstitution", "UniversityOfKansasCenterForResearchInc"], "Investigators" -> {Entity["NSFInvestigator", "SuzanneShontz"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "1187", "Text" -> "PECASE- eligible"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Direct For Computer & Info Scie & Enginr", "Division" -> "Div Of Advanced Cyberinfrastructure", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500487&HistoricalAwards=false"], "KeywordTally" -> {{"IVC", 8}, {"blood", 5}, {"develop", 4}, {"dynamic", 4}, {"filter", 4}, {"meshes", 4}, {"meshing", 4}, {"parallel", 4}, {"algorithms", 3}, {"clots", 3}, {"filters", 3}, {"investigators", 3}, {"accurate", 2}, {"clot", 2}, {"computational", 2}, {"deep", 2}, {"deformations", 2}, {"developed", 2}, {"DVT", 2}, {"form", 2}, {"generate", 2}, {"improved", 2}, {"mesh", 2}, {"order", 2}, {"patient-specific", 2}, {"simulations", 2}, {"software", 2}, {"surrounding", 2}, {"techniques", 2}, {"use", 2}, {"vein", 2}, {"veins", 2}}|>, "1500508" -> <|"AwardTitle" -> "Applications of Non-Commutative Geometry", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2020, 6, 30}], "AwardAmount" -> Quantity[42453, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "One of the central themes of modern mathematics has been the fusion of geometry and algebra. This began in the seventeenth century with Rene Descartes's remarkable insight that associated to any equation a geometric object; namely, the graph of the equation. Geometric properties of the graph encode algebraic properties of the equation, and vice versa. Throughout the eighteenth, nineteenth, and twentieth centuries, many mathematicians worked to deepen and extend Descartes's ideas. Thus the subject of algebraic geometry was developed. This subject has flourished and has achieved many outstanding results. In the mid-twentieth century--largely inspired by quantum theory and other physics--a new kind of algebra (operator algebras) emerged. More recently, this new algebra has been combined with geometry to form the new subject of noncommutative geometry. The mathematics of this project takes methods and results from noncommutative geometry and applies them to problems in the older, more traditional branches of mathematics.\n\nThe noncommutative geometry point of view has led to some startling conjectures and results. In the representation theory of reductive p-adic groups a totally unexpected geometric structure has been revealed. This greatly simplifies the representation theory and links the Baum-Connes conjecture (which is a conjecture within noncommutative geometry) to the Langlands program. For the index of geometrically-arising Fredholm operators, the noncommutative geometry point of view leads to the surprising conclusion that formulas like the Atiyah-Singer index formula apply well beyond elliptic operators. Hence ellipticity is not the essential point needed to obtain a topological formula for the index of such operators. This project will explore the many interactions of this wide-ranging set of ideas.", "AwardID" -> "1500508", "Institution" -> Entity["NSFInstitution", "PennsylvaniaStateUnivUniversityPark"], "Investigators" -> {Entity["NSFInvestigator", "PaulBaum"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500508&HistoricalAwards=false"], "KeywordTally" -> {{"geometry", 8}, {"noncommutative", 5}, {"algebra", 3}, {"equation", 3}, {"index", 3}, {"new", 3}, {"operators", 3}, {"point", 3}, {"results", 3}, {"subject", 3}, {"theory", 3}, {"algebraic", 2}, {"century", 2}, {"conjecture", 2}, {"Descartes's", 2}, {"formula", 2}, {"geometric", 2}, {"graph", 2}, {"ideas", 2}, {"mathematics", 2}, {"project", 2}, {"properties", 2}, {"representation", 2}, {"view", 2}}|>, "1500509" -> <|"AwardTitle" -> "Applications of Harmonic Analysis to Function Theory and Operator Theory", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2015, 10, 31}], "AwardAmount" -> Quantity[116697, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This research project will conduct a study of fundamental questions in function theory and operator theory using the tools and techniques of harmonic analysis. The project will address important questions now open to exploration because of recent advances made by the principal investigator and his collaborators. Resolution of these problems raised will find applications in function theoretic operator theory and yield new tools and techniques that can be adopted by the larger analysis community. The principal investigator will advise graduate students and postdoctoral fellows, include them in the proposed research projects, and provide mentoring, in order to assist them in transitioning to the next stage of their careers. Broad dissemination of the results will take place by participation in conferences and posting of the research to the arxiv preprint server.\n\nThis project will combine recent results of the principal investigator with motivation from function theory and operator theory to study questions related to the two-weight Hilbert transform and properties of model spaces. The first research direction to be explored couples the results of the principal investigator with questions about boundedness and invertibility properties of products of Toeplitz operators. In particular, the problems to be studied are aimed at obtaining a better understanding of the composition of paraproducts and determining necessary and sufficient conditions for their boundedness. Connections to the two-weight inequality for the Hilbert transform suggest related problems to investigate. Resolving the proposed problems will provide more insight into the recent characterization of the two-weight inequality for the Hilbert transform and related properties for Toeplitz operators on the Hardy space. An additional research direction, based upon the principal investigator's recent results and their connection to the description of the Carleson measure for model spaces, will be pursued. The open question of obtaining a characterization of the Riesz bases for model spaces leads to problems related to reverse Carleson measures for the model spaces, and their relation to two-weight inequalities for the Cauchy and Hilbert transforms. Additional directions of investigation connect to bilinear forms and commutators on model spaces.", "AwardID" -> "1500509", "Institution" -> Entity["NSFInstitution", "GeorgiaTechResearchCorporation"], "Investigators" -> {Entity["NSFInvestigator", "BrettWick"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500509&HistoricalAwards=false"], "KeywordTally" -> {{"model", 5}, {"principal", 5}, {"problems", 5}, {"research", 5}, {"spaces", 5}, {"theory", 5}, {"Hilbert", 4}, {"investigator", 4}, {"questions", 4}, {"recent", 4}, {"related", 4}, {"results", 4}, {"-weight", 4}, {"function", 3}, {"operator", 3}, {"project", 3}, {"properties", 3}, {"transform", 3}, {"analysis", 2}, {"boundedness", 2}, {"Carleson", 2}, {"characterization", 2}, {"direction", 2}, {"inequality", 2}, {"obtaining", 2}, {"open", 2}, {"operators", 2}, {"proposed", 2}, {"provide", 2}, {"study", 2}, {"techniques", 2}, {"Toeplitz", 2}, {"tools", 2}}|>, "1500511" -> <|"AwardTitle" -> "LSAMP Bridge to the Doctorate at UMBC (2015-2017)", "AwardEffectiveDate" -> DateObject[{2015, 4, 15}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Tasha Inniss", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the Science, Technology, Engineering, and Mathematics (STEM) workforce through the development of highly competitive students from groups historically underrepresented in STEM disciplines: African-Americans, Alaska Natives, American Indians, Hispanic Americans, Native Hawaiians, and Native Pacific Islanders. The goal of the LSAMP Bridge to the Doctorate (BD) Activity is to increase the quantity and quality of STEM graduate students from underrepresented populations, with emphasis on Ph.D. matriculation and completion. For the U.S. to remain globally competitive, it is vital that it taps into the talent of all its citizens and provides exceptional educational preparedness in STEM areas that underpin the knowledge-based economy. BD programs implemented in the nation's institutions of higher education contribute to addressing one of the objectives in NSF's 2014-2018 Strategic Plan, namely to \"integrate education and research to support development of a diverse STEM workforce with cutting-edge capabilities.\" The University of Maryland Baltimore County (UMBC), lead institution of PROMISE: MD's Alliance for Graduate Education and the Professoriate (AGEP) and the University System of Maryland (USM) LSAMP, will be the host site for the 2015-2017 USM BD Program. The activities of UMBC's program provide BD Fellows with a positive doctoral experience that includes meaningful initiatives such as professional leadership, community networking, and improved discipline-specific group and individual mentoring that have demonstrated positive impact on retention and successful graduation. Therefore, the efforts at UMBC will continue to contribute to increasing the diversity and representation in academia and the STEM workforce, thereby increasing the nation's competitiveness.\n\nThe proposed training for the 2015-2017 cohort of BD Fellows is extensive. The academic departments at UMBC have enthusiastically embraced the BD Program and are true partners in the success of the BD Fellows who will be heavily mentored to ensure they receive strong academic and professional preparation. UMBC's BD Fellows are provided excellent training in core competencies in their disciplines. The BD Fellows will also have the opportunity, early in their academic careers, to conduct cutting-edge research with top research scientists on campus and at national laboratories located in close proximity to UMBC. The proposed activities such as the required university-wide and state-wide research presentations, and training for participation in national and international research efforts, provide the BD Fellows with creative ways to enhance their preparation for STEM careers. Furthermore, the planned training in leadership, teaching, and mentoring will position the fellows well for future faculty positions, or other areas of the STEM workforce. The team has worked cohesively to facilitate the success of BD Fellows since 2005 and Alliances for Graduate Education and the Professoriate (AGEP) students since 2003. Since the first BD cohort matriculated at UMBC in 2005, 108 BD Fellows have enrolled in STEM graduate programs at UMBC and at the University of Maryland, College Park. USM BD Fellows have earned 9 STEM Ph.Ds. and 47 master's degrees; 63 Fellows are currently persisting in an MS or Ph.D. program (17 students in master's programs and 46 students in doctoral programs).", "AwardID" -> "1500511", "Institution" -> Entity["NSFInstitution", "UniversityOfMarylandBaltimoreCounty"], "Investigators" -> {Entity["NSFInvestigator", "FreemanHrabowski"], Entity["NSFInvestigator", "JanetRutledge"], Entity["NSFInvestigator", "CynthiaHILL"], Entity["NSFInvestigator", "RenettaTull"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500511&HistoricalAwards=false"], "KeywordTally" -> {{"BD", 14}, {"Fellows", 10}, {"STEM", 10}, {"UMBC", 6}, {"research", 5}, {"students", 5}, {"programs", 4}, {"training", 4}, {"workforce", 4}, {"academic", 3}, {"LSAMP", 3}, {"Maryland", 3}, {"program", 3}, {"University", 3}, {"USM", 3}, {"2005", 2}, {"2015-2017", 2}, {"activities", 2}, {"AGEP", 2}, {"Alliances", 2}, {"areas", 2}, {"careers", 2}, {"cohort", 2}, {"competitive", 2}, {"contribute", 2}, {"cutting-edge", 2}, {"development", 2}, {"disciplines", 2}, {"doctoral", 2}, {"education", 2}, {"Education", 2}, {"efforts", 2}, {"graduate", 2}, {"Graduate", 2}, {"increasing", 2}, {"leadership", 2}, {"master's", 2}, {"mentoring", 2}, {"national", 2}, {"nation's", 2}, {"Native", 2}, {"Ph.D.", 2}, {"positive", 2}, {"preparation", 2}, {"professional", 2}, {"Professoriate", 2}, {"Program", 2}, {"proposed", 2}, {"provide", 2}, {"success", 2}, {"UMBC's", 2}, {"underrepresented", 2}}|>, "1500513" -> <|"AwardTitle" -> "Texas A&M University System Louis Stokes Alliance for Minority Participation (TAMUS LSAMP) Bridge to the Doctorate (BTD) Cohort XI (2015 - 2017) Program", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2017, 4, 30}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Dr. A. James Hicks", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the Science, Technology, Engineering, and Mathematics (STEM) workforce through the development of highly competitive students from groups historically underrepresented in STEM disciplines: African-Americans, Alaska Natives, American Indians, Hispanic Americans, Native Hawaiians, and Native Pacific Islanders. The goal of the LSAMP Bridge to the Doctorate (BD) Activity is to increase the quantity and quality of STEM graduate students from underrepresented populations, with emphasis on Ph.D. matriculation and completion. For the U.S. to remain globally competitive, it is vital that it taps into the talent of all its citizens and provides exceptional educational preparedness in STEM areas that underpin the knowledge-based economy. Texas A&M University, lead institution of the Texas A&M University System (TAMUS) LSAMP, will host their 11th cohort of BD Fellows. The goal of the program is to foster academic success in a cohort of twelve first-time underrepresented STEM graduate students by developing their readiness and encouraging eagerness to complete STEM doctoral degrees and by preparing them to take their place as leaders in interdisciplinary research and in academia. By increasing the number of well-prepared and highly qualified Ph.Ds that ultimately enter the STEM workforce, TAMUS LSAMP BTD program has the potential to contribute significantly to the increase of this nation's economy and prosperity.\n\nThe objectives of the TAMUS LSAMP BD Program will be achieved through collaborations among the College of Science (COS), the Dwight Look College of Engineering (COE), the College of Agriculture and Life Sciences (COALS), and the College of Geosciences (COG) at TAMU. The five major components of the program are (1) professional development, (2) academic support and social integration, (3) mentoring, (4) leadership development, and (5) student support and community building. The twelve BD Fellows with differing STEM disciplines and a common purpose will be nurtured for two years as a cohorted community and will share coordinated resources and intellectually enriching group activities with each other, and also with the larger population of STEM graduate students at TAMU, for the benefit of all. The objectives of the program include (1) retention of fellows into doctoral programs with funding after completion of the two-year NSF BD program, (2) preparation of fellows to meet the challenges of completing STEM doctoral programs and for possible academic careers in higher education, and (3) leadership skill development necessary to succeed as young STEM professionals upon completion of doctoral programs of study. Out of the 60 BD fellows supported in the first five cohorts at TAMU, 26 have completed their Ph.Ds. in STEM and 12 are progressing well towards the doctoral degree.", "AwardID" -> "1500513", "Institution" -> Entity["NSFInstitution", "TexasA&MEngineeringExperimentStation"], "Investigators" -> {Entity["NSFInvestigator", "KarenButler-Purry"], Entity["NSFInvestigator", "ShannonWalton"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500513&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 12}, {"BD", 6}, {"program", 6}, {"doctoral", 5}, {"LSAMP", 5}, {"College", 4}, {"development", 4}, {"students", 4}, {"academic", 3}, {"completion", 3}, {"fellows", 3}, {"graduate", 3}, {"programs", 3}, {"TAMU", 3}, {"TAMUS", 3}, {"underrepresented", 3}, {"1", 2}, {"2", 2}, {"3", 2}, {"cohort", 2}, {"community", 2}, {"competitive", 2}, {"disciplines", 2}, {"economy", 2}, {"Engineering", 2}, {"Fellows", 2}, {"five", 2}, {"goal", 2}, {"highly", 2}, {"increase", 2}, {"leadership", 2}, {"&M", 2}, {"Native", 2}, {"objectives", 2}, {"Ph.Ds", 2}, {"Science", 2}, {"support", 2}, {"Texas", 2}, {"twelve", 2}, {"University", 2}, {"workforce", 2}}|>, "1500517" -> <|"AwardTitle" -> "Applied Inverse Problems 2014 Conference Finland", "AwardEffectiveDate" -> DateObject[{2015, 1, 1}], "AwardExpirationDate" -> DateObject[{2015, 12, 31}], "AwardAmount" -> Quantity[30000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Abstract (Uhlmann, 1500517): \n\nThe award will support graduate students and postdoctoral researchers to participate in the Applied Inverse problems 2015 (AIP 2015), be held in Helsinki, Finland, May 25-29, 2015, as well as a summer school held also in Helsinki, May 19-22, 2015.\n\nAIP 2015 is one of a series of AIP Conferences aimed to provide a primary international forum for academic and industrial researchers working on all aspects of inverse problems, such as mathematical modelling, analytic and geometric methods, computational approaches, numerical algorithms etc. It will cover a broad spectrum of the applications of inverse problems, focusing on recent developments in medical imaging, determination of defects in materials homogenization and inverse problems, geometric inverse problems, remote sensing, industrial applications, numerical and regularization methods in inverse problems, and also, invisibility and cloaking. More information of the conference can be found at the website http://aip2015.fips.fi/. The NSF support from this award will allow a financial package for US students and postdocs to participate in the conference and the summer school, and will significantly enhance the ability to recruit an outstanding and diverse group of researchers to work in the area of inverse problems.", "AwardID" -> "1500517", "Institution" -> Entity["NSFInstitution", "UniversityOfWashington"], "Investigators" -> {Entity["NSFInvestigator", "GuntherUhlmann"]}, "ProgramElements" -> {{"Code" -> "1266", "Text" -> "APPLIED MATHEMATICS"}, {"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500517&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 7}, {"inverse", 6}, {"2015", 4}, {"researchers", 3}, {"AIP", 2}, {"applications", 2}, {"award", 2}, {"conference", 2}, {"geometric", 2}, {"held", 2}, {"Helsinki", 2}, {"industrial", 2}, {"methods", 2}, {"numerical", 2}, {"participate", 2}, {"school", 2}, {"students", 2}, {"summer", 2}, {"support", 2}}|>, "1500518" -> <|"AwardTitle" -> "Plasma-Surface Interactions During In-Situ Photo-Assisted Etching", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[145000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "Reactive ion etching (or plasma etching) is a critical operation in the manufacturing of integrated circuits (or 'chips') to produce extremely precise features, at the nanometer (a billionth of a meter) scale. Without this process we would have no portable cell phones, laptop computers and all the other modern marvels we take for granted. Ever smaller feature dimensions will allow more transistors to be packed onto chips, resulting in increased information storage and faster computers. This evolution in chip speed and function has progressed steadily over the past 50 years, following Moore's Law, which states that the number of transistors on a chip doubles about every 18 months. Recently, while studying reactive ion etching of silicon, a rather startling discovery was made: silicon was etched, even when no reactive ions were present. Careful experiments revealed that this etching was due to photons, originating in the plasma. This in-plasma photo-assisted etching produced etched feature shapes that are not optimum for integrated circuits and thus may prove to be a show-stopper in the burgeoning field of etching with atomic precision. This project will combine experiments and simulations to understand the mechanism of in-plasma photo-assisted etching, and identify conditions to suppress this phenomenon. The study will produce a fundamental understanding of the photo-physics and chemistry at the plasma-semiconductor interface and will have a significant impact in the microelectronics industry as well as the field of nanotechnology, with clear societal benefits.\n\nThis systematic investigation of plasma-surface interactions will focus on in-situ photon-plasma synergism, and its effect on etching of semiconductor materials in halogen-containing plasmas. A combination of experiments and simulations will address questions such as: (a) What are the synergistic effects of photons and i) positive ions, ii) electrons, iii) negative ions, iv) halogen atoms? (b) does the sheath potential affect photo-assisted etching rates and if so, how and what is the cause? (c) what is the effect of surface plasmons (plasmonics) in the case of samples patterned with sub-wavelength features? A novel dual plasma reactor will be employed, to provide controlled fluxes of ions, UV-VUV photons, and radicals bombarding the substrate. The UV-VUV light intensity, ion flux and ion energy striking the substrate will be measured through a pinhole on the substrate holder, in a differentially pumped analysis chamber. Self-consistent simulations of the electric field distribution and species (electrons, holes, positive ions) fluxes in the plasma as well as in the solid, and electromagnetic calculations of surface plasmon propagation and absorption will be performed. Simulations coupled with experiments will provide insights in the mechanism of photo-assisted etching for varying substrate bias (potential of the sheath over the semiconductor), photon flux and energy, dopant concentration, as well as nanofeature size and aspect ratio. Finally, attempts will be made to exploit photo-assisted etching of silicon to create nanoholes with dimensions (e.g., 3 nm dia.) much smaller than those produced by conventional reactive ion etching.", "AwardID" -> "1500518", "Institution" -> Entity["NSFInstitution", "UniversityOfHouston"], "Investigators" -> {Entity["NSFInvestigator", "DemetreEconomou"], Entity["NSFInvestigator", "VincentDonnelly"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500518&HistoricalAwards=false"], "KeywordTally" -> {{"etching", 12}, {"ion", 5}, {"ions", 5}, {"photo-assisted", 5}, {"experiments", 4}, {"plasma", 4}, {"substrate", 4}, {"field", 3}, {"photons", 3}, {"reactive", 3}, {"silicon", 3}, {"simulations", 3}, {"chip", 2}, {"chips", 2}, {"circuits", 2}, {"computers", 2}, {"dimensions", 2}, {"effect", 2}, {"electrons", 2}, {"energy", 2}, {"etched", 2}, {"feature", 2}, {"features", 2}, {"flux", 2}, {"fluxes", 2}, {"integrated", 2}, {"mechanism", 2}, {"-plasma", 2}, {"positive", 2}, {"potential", 2}, {"produce", 2}, {"produced", 2}, {"provide", 2}, {"semiconductor", 2}, {"sheath", 2}, {"smaller", 2}, {"surface", 2}, {"transistors", 2}, {"UV-VUV", 2}}|>, "1500519" -> <|"AwardTitle" -> "North Carolina LSAMP Bridge to the Doctorate Program at NCA&T (2015-2017)", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[986982, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Martha L. James", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the STEM workforce through the development of highly competitive students from groups historically underrepresented in STEM disciplines: African-Americans, Alaska Natives, American Indians, Hispanic Americans, Native Hawaiians, and Native Pacific Islanders. The goal of the LSAMP Bridge to the Doctorate (BD) Activity is to increase the quantity and quality of STEM graduate students from underrepresented populations, with emphasis on Ph.D. matriculation and completion. For the U.S. to remain globally competitive, it is vital that it taps into the talent of all its citizens and provides exceptional educational preparedness in STEM areas that underpin the knowledge-based economy. North Carolina Agricultural and Technical State University (NCA&T), a Historically Black University and lead institution for the North Carolina LSAMP (NCLSAMP), will serve as the host institution for the 2015-2017 cohort of BD Fellows. The NCLSAMP BD Program is designed to assist students' academic and social integration into the graduate school culture through a structured advisement and mentoring model. The strategies employed will contribute to the goal of increasing the quantity of well-trained, highly-skilled STEM professionals from underrepresented groups. Ultimately, these efforts would enhance diversity and representation in academia and the STEM workforce, thereby increasing the nation's competitiveness.\n\nThe overall objectives of the BD Program at NCA&T are to recruit nationally a cohort of 12 former LSAMP students into STEM graduate programs at NCA&T and demystify the graduate degree process through intensive academic enrichment, professional development, involvement in faculty-led research, and mentoring. The activities, which are designed to assist the successful transition and retention of the BD Fellows, include: (i) regularly scheduled meetings with BD staff; (ii) financial support to attend and participate in professional meetings and seminars; (iii) active engagement in research during the academic year and summer; (iv) presentations at national conferences; (v) visitations to graduate research laboratories at other research-intensive institutions; and (vi) intensive preparation for application to selected STEM doctoral degree programs.", "AwardID" -> "1500519", "Institution" -> Entity["NSFInstitution", "NorthCarolinaAgricultural&TechnicalStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "SanjivSarin"], Entity["NSFInvestigator", "MarciaWilliams"], Entity["NSFInvestigator", "JoeWhitehead"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500519&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 8}, {"BD", 6}, {"graduate", 5}, {"LSAMP", 4}, {"students", 4}, {"academic", 3}, {"NCA&T", 3}, {"research", 3}, {"underrepresented", 3}, {"assist", 2}, {"Carolina", 2}, {"cohort", 2}, {"competitive", 2}, {"degree", 2}, {"designed", 2}, {"development", 2}, {"Fellows", 2}, {"goal", 2}, {"groups", 2}, {"increasing", 2}, {"institution", 2}, {"intensive", 2}, {"meetings", 2}, {"mentoring", 2}, {"Native", 2}, {"NCLSAMP", 2}, {"North", 2}, {"professional", 2}, {"Program", 2}, {"programs", 2}, {"quantity", 2}, {"University", 2}, {"workforce", 2}}|>, "1500525" -> <|"AwardTitle" -> "Studies in Moduli Theory and Birational Geometry", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[115925, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "The area of study of this project lies within algebraic geometry, the branch of mathematics devoted to geometric shapes called algebraic varieties, defined by polynomial equations. Algebraic geometry has significant applications in coding, industrial control, and computation. But the topics of this project are more closely related to applications in theoretical physics, where physicists consider algebraic varieties as a piece of the fine structure of our universe. This is especially true with the first topic, moduli theory. This theory studies a remarkable phenomenon in which the collection of all algebraic varieties of the same type is manifested as an algebraic variety, called a moduli space, in its own right. Thus in algebraic geometry, the metaphor of thinking about a community of \"organisms\" as itself being an \"organism\" is not just a metaphor but a rigorous and quite useful fact. The other topic studied in this project is birational geometry, which is devoted to a certain abstract relationship, called birational equivalence, among algebraic varieties, which lies at the foundation of algebraic geometry.\n\nThe investigator will continue studying problems in moduli theory; the main foci of the project are Moduli spaces of stable logarithmic maps and Artin fans. Additional topics include the degeneration formula for KKO invariants, the birational geometry of torus quotients, and logarithmic Kodaira dimensions of fibered powers in relation to uniformity of stably integral points.", "AwardID" -> "1500525", "Institution" -> Entity["NSFInstitution", "BrownUniversity"], "Investigators" -> {Entity["NSFInvestigator", "DanAbramovich"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500525&HistoricalAwards=false"], "KeywordTally" -> {{"algebraic", 8}, {"geometry", 5}, {"project", 4}, {"varieties", 4}, {"birational", 3}, {"called", 3}, {"moduli", 3}, {"theory", 3}, {"applications", 2}, {"devoted", 2}, {"lies", 2}, {"logarithmic", 2}, {"metaphor", 2}, {"topic", 2}, {"topics", 2}}|>, "1500529" -> <|"AwardTitle" -> "Mutual Mentoring to Reduce Isolation in Physics", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2020, 8, 31}], "AwardAmount" -> Quantity[742648, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "dana britton", "Abstract" -> "The PLAN-D funding track is designed to expand the application of proven-successful gender-equity initiatives for STEM faculty in a specific disciplinary area through networked adaptation of a specific program or initiative. Careful evaluation is expected to expand understanding of such initiatives in a disciplinary context.\n\nThis project will create mutual mentoring eAlliances for professional development under the auspices of the American Association of Physics Teachers (AAPT) by developing ten alliances of women physics faculty who are isolated in various ways. This intervention will directly impact the careers of the fifty women physics faculty members who participate in the mutual mentoring alliances supported by this project. eAlliance participants will meet initially in-person at professional meetings followed by regular electronic meetings. This project will reduce the isolation of participating physicists and provide support to enhance their career development. The project evaluation will identify the benefits of mutual mentoring networks, particularly for isolated faculty, and add to the research on the impact of mutual mentoring on career development.\n\nThe project will develop and test a cost-effective model for mentoring for physics educators which could be adapted for other academic scientists and other work environments. eAlliances of mutual mentors will aid in the professional development of participants who are isolated by virtue of gender, race, sexual orientation, and/or type of institution. This project is based on past ADVANCE projects and research on the effects of isolation and good mentoring practices. The project has the potential to enhance retention and job satisfaction of isolated physics faculty. This project will work toward institutionalizing these mentoring networks within AAPT. Because the project will be implemented by the AAPT, the project will help to professionalize and highlight the importance of mentoring within the physics community.\n\nThe NSF ADVANCE Partnerships for Learning and Adaptation Networks (PLAN) program track supports projects that promote the adaptation and implementation of previously effective ADVANCE programs in new contexts and the testing of innovative strategies to promote the participation, success, and advancement of women in STEM academic careers. PLAN projects also contribute to the knowledge base on gender equity in STEM academic careers.", "AwardID" -> "1500529", "Institution" -> Entity["NSFInstitution", "AmericanAssociationOfPhysicsTeachers"], "Investigators" -> {Entity["NSFInvestigator", "BarbaraWhitten"], Entity["NSFInvestigator", "AnneCox"], Entity["NSFInvestigator", "BethCunningham"], Entity["NSFInvestigator", "CynthiaBlaha"], Entity["NSFInvestigator", "IdaliaRamos"]}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500529&HistoricalAwards=false"], "KeywordTally" -> {{"project", 10}, {"mentoring", 8}, {"faculty", 5}, {"mutual", 5}, {"physics", 5}, {"isolated", 4}, {"AAPT", 3}, {"academic", 3}, {"ADVANCE", 3}, {"careers", 3}, {"development", 3}, {"professional", 3}, {"projects", 3}, {"STEM", 3}, {"women", 3}, {"adaptation", 2}, {"alliances", 2}, {"career", 2}, {"disciplinary", 2}, {"eAlliances", 2}, {"enhance", 2}, {"evaluation", 2}, {"expand", 2}, {"gender", 2}, {"impact", 2}, {"initiatives", 2}, {"isolation", 2}, {"meetings", 2}, {"networks", 2}, {"participants", 2}, {"PLAN", 2}, {"program", 2}, {"promote", 2}, {"research", 2}, {"specific", 2}, {"track", 2}, {"work", 2}}|>, "1500535" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Reassessing the role of the Great American Biotic Interchange in the evolution of the raccoon family", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 5, 31}], "AwardAmount" -> Quantity[16549, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010206", "ProgramOfficer" -> "Simon Malcomber", "Abstract" -> "The Great American Biotic Interchange (GABI) was a major biogeographic event that connected the terrestrial animal communities of North and South America via the closure of the Panamanian Isthmus. Geological evidence and the fossil record have suggested that the closure of the isthmus occurred 3 million years ago (mya), but more recent studies suggest a much older age for the formation of a landbridge between North and South America, around 15 mya. Among mammals of North American origin, the raccoon family (Procyonidae), which also includes coatis, kinkajous, olingos, and ringtails, has one of the longest histories in South America. The fossil record shows that an extinct member of this group was the first North American mammal to immigrate to South America, approximately 7-9 mya. While the prevailing hypothesis states that immigration of modern members of this group took place 3 mya, recent estimates based on DNA sequence data revealed that this family has had a much longer tenure in South America. This study will more thoroughly test competing hypotheses regarding the process and timing of evolution of this group, with the potential to revise our understanding of mammal evolution in the Neotropics, while contributing to advancement in the fields of genomics, systematics, taxonomy, and biogeography, as well as promoting the professional development of an early-career female STEM researcher. \n\nThis project will use an integrative approach to test competing hypotheses based on genomic analyses of museum specimens, morphometrics, and biogeographic modeling. Ancient DNA techniques in combination with high-throughput sequencing methods will be used to sequence mitochondrial genomes as well as to sample the nuclear genome using a novel intron-capture microarray. Morphometric data will be analyzed separately and in conjunction with comparative genomic data to test hypotheses regarding procyonid evolution and revise the taxonomy of this group. A new biogeographic model for the evolution of the raccoon family that accommodates the most recent DNA and geological evidence will be tested against the traditional fossil-based hypothesis, and will integrate phylogenetic data to reassess the tempo and geographic pattern of diversification associated with the GABI. Results will be shared through scientific publications co-authored by the PI, Co-PI, and collaborators. Genomic and morphological data, protocols, scripts and parameters used in the analyses will be made publicly available through the electronic repositories of NCBI?s Genbank and Dryad.", "AwardID" -> "1500535", "Institution" -> Entity["NSFInstitution", "GeorgeMasonUniversity"], "Investigators" -> {Entity["NSFInvestigator", "AndreaWeeks"], Entity["NSFInvestigator", "MirianTiekoNunesTsuchiya"]}, "ProgramElements" -> {{"Code" -> "1171", "Text" -> "PHYLOGENETIC SYSTEMATICS"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500535&HistoricalAwards=false"], "KeywordTally" -> {{"America", 5}, {"data", 5}, {"South", 5}, {"evolution", 4}, {"group", 4}, {"mya", 4}, {"North", 4}, {"American", 3}, {"biogeographic", 3}, {"DNA", 3}, {"family", 3}, {"hypotheses", 3}, {"recent", 3}, {"test", 3}, {"3", 2}, {"analyses", 2}, {"based", 2}, {"closure", 2}, {"competing", 2}, {"evidence", 2}, {"fossil", 2}, {"GABI", 2}, {"genomic", 2}, {"hypothesis", 2}, {"mammal", 2}, {"raccoon", 2}, {"record", 2}, {"regarding", 2}, {"revise", 2}, {"sequence", 2}, {"taxonomy", 2}, {"used", 2}}|>, "1500538" -> <|"AwardTitle" -> "Collaborative Research: Experimental and Theoretical Study of the Plasma Physics of Antihydrogen Generation and Trapping", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[15000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "The long-term goals of this research address the very basis of our understanding of the world around us. Potentially, it has deep implications on the nature of particle interactions, on the question of matter-antimatter symmetry, and on cosmology. At the same time, this research is uniquely visible because the study of antimatter is accessible and fascinating to the public. Antihydrogen experiments are sufficiently simple that they can be comprehended in their entirety by graduate students. Consequently, they offer students a broad education. Experimental students learn beam and plasma physics, experimental planning and design, instrumentation, electronics, cryogenics, magnetics and software development. Along with theory development, theory students can make critical contributions to the design, operation, and analysis of the experiments. The relative accessibility of the material makes it easy to integrate undergraduate students into both the experimental and theoretical program. The research includes significant participation by members of underrepresented groups.\n\nThe research is primarily focused on the immediate plasma and atomic physics issues surrounding improving the trapping of antihydrogen, and on the design of a third generation trap optimized for gravitational research. The physics issues will be studied with experiments at Berkeley and at CERN, with classical trajectory Monte Carlo, molecular dynamics, Vlasov codes and 3D Particle-In-Cell codes, and with analytic theory. Some of the questions that will be addressed include: achieving improved (lower) lepton and antiproton temperatures; studying how leptons interact with the background radiation field; studying how leptons interact with resonant cavities; improved plasma diagnostics; and improved mixing of positrons and antiprotons, so that more of the resultant antihydrogen can be held in a very shallow neutral trap. While the motivation for seeking answers to these questions comes from antihydrogen research, many of these questions raise novel and deep issues in plasma and atomic physics. This research is co-sponsored by the NSF's Physics Division and the Office of International Science and Engineering.", "AwardID" -> "1500538", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Berkeley"], "Investigators" -> {Entity["NSFInvestigator", "JonathanWurtele"], Entity["NSFInvestigator", "JoelFajans"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500538&HistoricalAwards=false"], "KeywordTally" -> {{"research", 7}, {"students", 5}, {"physics", 4}, {"plasma", 4}, {"antihydrogen", 3}, {"design", 3}, {"experiments", 3}, {"improved", 3}, {"issues", 3}, {"questions", 3}, {"theory", 3}, {"atomic", 2}, {"codes", 2}, {"deep", 2}, {"development", 2}, {"experimental", 2}, {"interact", 2}, {"leptons", 2}, {"studying", 2}, {"trap", 2}}|>, "1500545" -> <|"AwardTitle" -> "Metrics, Measures, and Identities on Moduli Spaces", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[118656, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "The PI studies the interconnections between the fields of geometry, physics, dynamics, statistics and number theory. A geometry on a space is a means of measuring distance in the space and can be thought of as giving the space a shape. One approach to studying the geometry on a space is to consider the geodesic flow; this is an object that generalizes the notion of a straight line to spaces that are curved. By studying the properties of this object much can be discovered about the geometry itself. For example, the question of how many flow paths close up is related to the distribution of prime numbers. Often different geometries can be placed on a space and thus one obtains a space of shapes. A natural question to ask is if this space of shapes can be given a nice shape itself. The PI proposes to study these geometries on the space of geometries and investigate their properties. The PI will continue his commitment to both undergraduate and graduate education. The PI will mentor graduate students and postdoctoral assistant professors on research related to the project. The PI will also give research talks, expository talks, minicourses and lecture series on material related to the proposal as well as organize conferences. \n\nThe research plan of the PI centers around the use of certain geometric measures to define structures on moduli spaces and representation varieties. Such measures include the Hausdorff measure on the limit set of a Kleinian group, geodesic currents, the Patterson-Sullivan measure of a Kleinian group, equilibrium measures defined using Themodynamics associated with representations of hyperbolic groups, and push-forwards of volume measures by certain geometrically defined functions. One area of study is Higher Teichmuller Theory which is the study of representation spaces of hyperbolic groups into semi-simple Lie groups. These are generalizations of the classical Teichmuller space. Using Thermodynamics, the PI and collaborators define a Pressure geometry on this Higher Teichmuller space. space. The PI proposes to study the geometric property of this metric including its curvature, metric completion, and isometry group. Another area of proposed study is geometric identities; these are equations that hold on a moduli space of geometries. The PI and collaborators derive such identities by studying the statistical properties of the geodesic flow on a hyperbolic manifold. The PI proposes to study these identities and their relation to other known identities.", "AwardID" -> "1500545", "Institution" -> Entity["NSFInstitution", "BostonCollege"], "Investigators" -> {Entity["NSFInvestigator", "MartinBridgeman"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500545&HistoricalAwards=false"], "KeywordTally" -> {{"space", 12}, {"PI", 10}, {"study", 6}, {"geometry", 5}, {"geometries", 4}, {"identities", 4}, {"measures", 4}, {"flow", 3}, {"geodesic", 3}, {"geometric", 3}, {"group", 3}, {"groups", 3}, {"hyperbolic", 3}, {"properties", 3}, {"proposes", 3}, {"related", 3}, {"research", 3}, {"spaces", 3}, {"studying", 3}, {"Teichmuller", 3}, {"area", 2}, {"certain", 2}, {"collaborators", 2}, {"define", 2}, {"defined", 2}, {"graduate", 2}, {"Higher", 2}, {"Kleinian", 2}, {"measure", 2}, {"metric", 2}, {"moduli", 2}, {"object", 2}, {"question", 2}, {"representation", 2}, {"shape", 2}, {"shapes", 2}, {"talks", 2}}|>, "1500562" -> <|"AwardTitle" -> "Automorphic Forms on Higher Rank and Kac-Moody Groups", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[75000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "Automorphic forms are a basic yet intricate structure in modern mathematics. Though historically they have been studied primarily by number theorists and representation theorists, they have connections to other branches of science. This research explores a number of questions connecting different areas of mathematics and physics. The project includes collaborative work with mathematical physicists that uses automorphic forms to describe corrections to general relativity that arise in string theory. \n\nOther projects include a detailed investigation of the square-integrability of certain Eisenstein residues (which has applications to the unitary dual problem), as well as a study of Eisenstein series on infinite-dimensional Kac-Moody group (in particular, the meromorphic continuation of their constant terms). Another project concerns applications of Voronoi-style summation formulas to number theory, such as to subconvexity problems for automorphic L-functions. Finally, the Miatello-Wallach conjecture (that the moderate growth condition in the theory of automorphic forms is in fact redundant on higher rank groups) will also be a focus of the research.", "AwardID" -> "1500562", "Institution" -> Entity["NSFInstitution", "RutgersUniversityNewBrunswick"], "Investigators" -> {Entity["NSFInvestigator", "StephenMiller"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500562&HistoricalAwards=false"], "KeywordTally" -> {{"automorphic", 3}, {"forms", 3}, {"number", 3}, {"theory", 3}, {"applications", 2}, {"Eisenstein", 2}, {"mathematics", 2}, {"project", 2}, {"research", 2}, {"theorists", 2}}|>, "1500572" -> <|"AwardTitle" -> "EAGER: Collaborative Research: Conceptualizing sustained environmental information management in the landscape of current and emerging eco-informatics infrastructure", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 3, 31}], "AwardAmount" -> Quantity[17158, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08080000", "ProgramOfficer" -> "Peter H. McCartney", "Abstract" -> "The data generated by environmental research are highly valuable, not only because of the cost of research but also because they are irreplaceable and needed for understanding change. A major challenge for all research entities is the management of this digital asset and associated information for maintaining its value. This challenge is complex in nature, covering not only the collection and storage of data, but also the creation of relevant (and sufficient) information about the data (metadata), such that they can be re-used broadly. Several environmental data repositories and data management approaches have been developed over the past few years. It is now time to seek input from researchers in the role of data authors and data re-users and data managers, to expansively explore the current operating environment, potential collaboration opportunities, efficiencies of scale, and future community needs for this challenge to be addressed effectively. An initial workshop will allow these stakeholders to share their expertise, experience and future requirements with their colleagues. The output from this initial exercise will then feed into a second session, which will result in strategic recommendations detailing the activities needed to create a collaborative and efficient data management infrastructure capable of supporting future environmental science research endeavors. \n\nMost current environmental data repositories fulfill specific needs or objectives, i.e., archiving and disseminating data from a project, network of research sites, institution, a specific funding source, or to accompany paper publications. Envisioning a sustained Scientific Data Infrastructure (SDI), and with the goal of providing high quality data to researchers, policy makers and the general public, this project concentrates on data repositories and current curation practices as an integral part of this vision. Within this scope and in the context of environmental research data management, original goals and objectives of single repositories will be re-evaluated, efficiencies of scale identified, a cost-benefit analyses for some centralized services attempted, and new, sustainable collaborations conceptualized. Specifically, data curators from a range of environmental research fields, data aggregators, tool developers, computer scientists and environmental scientists (both data providers and users) will be brought together for an informed dialog which draws on this broad collective experience. A preliminary information-gathering phase will describe the characteristics of each repository to inform the discussion at two subsequent community workshops. The first workshop will identify new collaboration and curation strategies that also cater to the currently underserved single investigators and move environmental data from \"available\" to \"usable\", in order to accelerate scientific inquiry. The second workshop will examine these strategies further, and develop one or more alternative, community-vetted roadmaps for research information management with the goal of more efficiently and sustainably utilizing NSF investments. In summary, these workshops will produce a strategic implementation plan outlining one or more options for a sustained environmental data management infrastructure capable of accelerating scientific inquiry, serve all contributing investigators (data producers) and provide the basis for education and outreach activities in a cost effective approach. Data management needs are fairly well understood. Organizational, personnel and management structures are not. Hence, the plan will focus on these challenges while also considering workforce development. A website for this project will be established at http://sedicollaborative.org.", "AwardID" -> "1500572", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-SantaBarbara"], "Investigators" -> {Entity["NSFInvestigator", "DanielReed"], Entity["NSFInvestigator", "MargaretOBrien"]}, "ProgramElements" -> {{"Code" -> "1165", "Text" -> "ADVANCES IN BIO INFORMATICS"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Div Of Biological Infrastructure", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500572&HistoricalAwards=false"], "KeywordTally" -> {{"data", 20}, {"environmental", 9}, {"management", 8}, {"research", 8}, {"repositories", 4}, {"challenge", 3}, {"current", 3}, {"future", 3}, {"information", 3}, {"needs", 3}, {"project", 3}, {"workshop", 3}, {"activities", 2}, {"capable", 2}, {"collaboration", 2}, {"community", 2}, {"cost", 2}, {"curation", 2}, {"Data", 2}, {"efficiencies", 2}, {"experience", 2}, {"goal", 2}, {"infrastructure", 2}, {"initial", 2}, {"inquiry", 2}, {"investigators", 2}, {"needed", 2}, {"new", 2}, {"objectives", 2}, {"plan", 2}, {"researchers", 2}, {"scale", 2}, {"scientific", 2}, {"scientists", 2}, {"second", 2}, {"single", 2}, {"specific", 2}, {"strategic", 2}, {"strategies", 2}, {"sustained", 2}, {"workshops", 2}}|>, "1500573" -> <|"AwardTitle" -> "Northwest Engineering and Vehicle Technology Exchange", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2017, 6, 30}], "AwardAmount" -> Quantity[199873, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11040100", "ProgramOfficer" -> "Elizabeth Teles", "Abstract" -> "The worldwide market for hybrid electric vehicle (HEV) and electric vehicle (EV) is growing steadily, with the United States taking the lead with over 500,000 HEV/EVs sold in 2013. This growth compounds when considered globally, with the forecast for the worldwide number of HEV/EVs on the in road in 2015 at 80.4 million. The west coast (Oregon, Washington and California) is the leader in HEV/EV ownership and development with nearly one-third (32.9%) of all HEV/EVs sales nationwide in these three states alone. This project at Central Oregon Community College (COCC) will prepare technicians to work in advanced HEV and EV diagnostics, maintenance, and repair. The establishment of a regional consortium, the Advanced Vehicle Training Group Northwest, will foster technology education opportunities for instructors and advanced automotive technicians across the northwest region. This collaboration will set and implement the standard for HEV/EV education. It will bring HEV/EV educational opportunities to rural students in Central Oregon, an area with a significant Latino and Native American population. \n\nThis project will support student learning in science and engineering technician education by developing new curriculum aligned with Society of Automotive Engineers (SAE) standards for HEV/EV certified training programs. This will add to the pedagogical knowledge in HEV/EV diagnostics, maintenance, and repair. In preparation for this effort, the college has conducted extensive research on automotive technology education gaps, has engaged in discussion with local and regional employers, has surveyed students and employers, and has investigated how other colleges statewide and nationally are addressing the HEV/EV education gap. This project will build on previously successful models for constructing alternative curricular pathways (often described as a latticed curriculum) to provide a rich tapestry of education and training opportunities for students at various stages of the employment cycle. It will also develop novel tools needed for alternative certification of skills through \"open badges.\" This national initiative is still early in development and every implementation of the badging process in a community college will add to the collective knowledge and understanding of best practices in the use of open badges to build a new curricular framework for educators in academic and industrial communities. A comprehensive evaluation plan will measures student success by completion rates for certifications, degrees, and badges earned. Outreach activities to underserved populations will focus on strategies known to be effective in reaching such students.", "AwardID" -> "1500573", "Institution" -> Entity["NSFInstitution", "CentralOregonCommunityCollege"], "Investigators" -> {Entity["NSFInvestigator", "BruceEmerson"], Entity["NSFInvestigator", "KennethMays"]}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Undergraduate Education", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500573&HistoricalAwards=false"], "KeywordTally" -> {{"HEV", 11}, {"EV", 8}, {"education", 6}, {"students", 4}, {"badges", 3}, {"EVs", 3}, {"opportunities", 3}, {"Oregon", 3}, {"project", 3}, {"add", 2}, {"advanced", 2}, {"alternative", 2}, {"automotive", 2}, {"build", 2}, {"Central", 2}, {"college", 2}, {"curricular", 2}, {"curriculum", 2}, {"development", 2}, {"diagnostics", 2}, {"electric", 2}, {"employers", 2}, {"knowledge", 2}, {"maintenance", 2}, {"new", 2}, {"open", 2}, {"regional", 2}, {"repair", 2}, {"student", 2}, {"technicians", 2}, {"technology", 2}, {"training", 2}, {"vehicle", 2}, {"worldwide", 2}}|>, "1500575" -> <|"AwardTitle" -> "Dynamical systems on nilmanifolds, ultrafilters, and polynomial multiple correlation sequences", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[157933, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "The problems and conjectures presented in this program can be viewed as far reaching extensions of classical recurrence results in dynamics. At the same time, these problems connect diverse areas of mathematics (such as ergodic theory, combinatorics, number theory, topological algebra) and contribute to each. The new problems considered in this proposal deal with interesting and promising new connections and reflect the entrance of novel methods and techniques in the picture. These include, in particular, the methods involving dynamical systems on nilmanifolds and methods utilizing the topological algebra in compactifications. The conjectures stated throughout this proposal are supported by the results obtained by the investigators and other workers in this vibrant area in recent years.\n\nThe polynomial Szemeredi theorem, the polynomial Hales-Jewett theorem, and various additional results obtained by the investigators in recent years served as an impetus for further developments in the theory of multiple recurrence. These developments provide better understanding of the phenomenon of multiple recurrence and bring new vistas of research to light. The directions of study touched upon in this proposal reveal strong and mutually perpetuating connections between combinatorics, number theory and various aspects of recurrence and convergence in the theory of dynamical systems. The field of Ergodic Ramsey Theory, with its richness of problems and connections and diversity of techniques and methods, is a meeting point of several branches of modern mathematics and is an excellent medium for attracting undergraduates to mathematics and graduate students to an area of active research.", "AwardID" -> "1500575", "Institution" -> Entity["NSFInstitution", "OhioStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "VitalyBergelson"], Entity["NSFInvestigator", "AlexanderLeibman"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500575&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 5}, {"methods", 4}, {"problems", 4}, {"recurrence", 4}, {"connections", 3}, {"mathematics", 3}, {"new", 3}, {"proposal", 3}, {"results", 3}, {"algebra", 2}, {"area", 2}, {"combinatorics", 2}, {"conjectures", 2}, {"developments", 2}, {"dynamical", 2}, {"investigators", 2}, {"multiple", 2}, {"number", 2}, {"obtained", 2}, {"polynomial", 2}, {"recent", 2}, {"research", 2}, {"systems", 2}, {"techniques", 2}, {"theorem", 2}, {"topological", 2}, {"various", 2}}|>, "1500579" -> <|"AwardTitle" -> "2015-2017 FGLSAMP Bridge to Doctorate at Florida International University", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2017, 7, 31}], "AwardAmount" -> Quantity[987000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "Dr. A. James Hicks", "Abstract" -> "The Louis Stokes Alliances for Minority Participation (LSAMP) program assists universities and colleges in diversifying the STEM workforce through their efforts at significantly increasing the numbers of students from historically underrepresented minority populations to successfully complete high quality degree programs in science, technology, engineering and mathematics (STEM) disciplines. The LSAMP Bridge to the Doctorate (LSAMP-BD) activity provides two-year support at the post baccalaureate level for students from historically underrepresented minority populations to matriculate in STEM graduate programs with the ultimate goal of earning a doctoral degree in a STEM discipline. Participants are selected from LSAMP institutions nationwide. The Florida-Georgia Louis Stokes Alliance for Minority Participation (Florida-Georgia LSAMP), under the leadership of Florida A & M University, a Historically Black College/University (HBCU), has chosen Florida International University (FIU), a Hispanic-serving institution (HSI) as the host for the 2015-2017 BD program in which a cohort of twelve LSAMP BD students will engage in STEM research, academics and professional development leading to completion of the STEM terminal degree. The programs promote systemic change in graduate education practices and policy in ways that increase the success of individual students on the doctoral pathway and the effectiveness of STEM graduate programs continuing the goal of diversifying America's STEM workforce.\n\nTwelve cohorts of students have matriculated in the Florida-Georgia LSAMP BD programs at the following sites: Florida State University, University of South Florida, University of Florida and Florida International University since 2003. For the 2015-2017 cohorts, the host of the Florida-Georgia LSAMP BD program will be Florida International University. The program includes collaborations and linkages with other STEM networks and resources as well as other graduate programs, such as NSF's Graduate Research Fellowship Program (GRFP) and other regional LSAMP-supported graduate education programs. The BD program at FIU provides a comprehensive set of support services that monitors student progress, builds a strong BD community, and increases BD students' academic and professional skills. Institutional resources are committed to ensure participants' successful completion of the STEM doctoral degree. This BD program will be externally evaluated and students will be tracked throughout its duration and into STEM careers following completion of STEM doctoral degree programs.", "AwardID" -> "1500579", "Institution" -> Entity["NSFInstitution", "FloridaAgriculturalAndMechanicalUniversity"], "Investigators" -> {Entity["NSFInvestigator", "RalphTurner"], Entity["NSFInvestigator", "ShekharBhansali"]}, "ProgramElements" -> {{"Code" -> "9133", "Text" -> "ALLIANCES-MINORITY PARTICIPAT."}}, "ProgramReferences" -> {{"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500579&HistoricalAwards=false"], "KeywordTally" -> {{"STEM", 12}, {"BD", 8}, {"programs", 8}, {"University", 8}, {"Florida", 7}, {"LSAMP", 7}, {"students", 7}, {"program", 6}, {"degree", 5}, {"graduate", 5}, {"doctoral", 4}, {"Florida-Georgia", 4}, {"completion", 3}, {"International", 3}, {"2015-2017", 2}, {"cohorts", 2}, {"diversifying", 2}, {"education", 2}, {"FIU", 2}, {"following", 2}, {"goal", 2}, {"historically", 2}, {"host", 2}, {"Louis", 2}, {"minority", 2}, {"Minority", 2}, {"Participation", 2}, {"populations", 2}, {"professional", 2}, {"provides", 2}, {"resources", 2}, {"Stokes", 2}, {"support", 2}, {"underrepresented", 2}}|>, "1500593" -> <|"AwardTitle" -> "Amenabilty, soficity, dynamics, and operator algebras", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[119998, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The subject of functional analysis provides a powerful mathematical language for the investigation of infinite-dimensional structures. The abstract nature of this language allows for a wide spectrum of applications, whose various settings include quantum mechanics, the theory of probability, and the study of systems, physical or otherwise, as they evolve in time. The project will concentrate on several aspects and generalized forms of the last of these three settings, and it will largely revolve around phenomena related to entropy.\n\nFinite or finite-dimensional approximation has long played a fundamental role in both dynamics and operator algebras and is manifest in its most basic and influential forms through the notions of amenability and soficity and their algebraic analogues. In the domain of C*-algebras, amenability has been subject to various refinements like finite decomposition rank and finite nuclear dimension that express the kind of topological regularity necessary for K-theoretic classification theorems within the Elliott program. This project aims to broaden our understanding of the relationships between these regularity properties and phenomena in topological dynamics, in particular mean dimension and Rokhlin-type dimensional invariants, and to test this understanding on a variety of examples that have so far remained beyond the scope of classification, such as actions of branch groups. Combinatorial independence will be brought into this picture as a tool for analyzing mixing and paradoxicality in dynamics and their relation to quasidiagonality and dimensional behavior, and it will be also applied to actions of sofic groups in the study of entropy and orbit equivalence.", "AwardID" -> "1500593", "Institution" -> Entity["NSFInstitution", "TexasA&MUniversityMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "DavidKerr"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500593&HistoricalAwards=false"], "KeywordTally" -> {{"dynamics", 3}, {"actions", 2}, {"algebras", 2}, {"amenability", 2}, {"classification", 2}, {"dimension", 2}, {"dimensional", 2}, {"finite", 2}, {"forms", 2}, {"groups", 2}, {"language", 2}, {"phenomena", 2}, {"project", 2}, {"regularity", 2}, {"settings", 2}, {"study", 2}, {"subject", 2}, {"topological", 2}, {"understanding", 2}, {"various", 2}}|>, "1500595" -> <|"AwardTitle" -> "Collaborative Research: Contributions of Endangered Language Data for Advances in Technology-enhanced Speech Annotation", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[235770, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Linguists have increased efforts to collect authentic speech materials from endangered and little-studied languages to discover linguistic diversity. However, the challenge of transcribing these speech into written form to facilitate analysis is daunting. This is because of both the sheer quantity of digitally collected speech that needs to be transcribed and the difficulty of unpacking the sounds of spoken speech. \n\nLinguist Andreas Kathol and computer scientist Vikramjit Mitra of SRI international and linguist Jonathan D. Amith of Gettysburg College will team up to create software that can substantially reduce the language transcription bottleneck. Using as a test case Yoloxochitl Mixtec, an endangered language from the state of Guerrero, Mexico, the team will develop a software tool that will use previously transcribed Yoloxochitl Mixtec speech data to both train a new generation of native speakers in practical orthography and to develop automatic speech recognition software. The output of the recognition software will be used as preliminary transcription that native speakers will correct, as necessary, to create additional high-quality training data. This recursive method will create corpus of transcribed speech large enough so that software will be able to complete automatic transcription of newly collected speech materials. \n\nThe project will include the training of undergraduate and graduate students in software development and the analysis of the Yoloxochitl Mixtec sound system. The project will also train native speakers as documenters in an interactive fashion that systematically introduces them to the transcription conventions of their language. This software tool will help in establishing literacy in Yoloxochitl Mixtec among a broader base of speakers. \n\nThe results of this project will be available at the Archive of Indigenous Languages of Latin America (University of Texas, Austin), Kaipuleohone (University of Hawai'i Digital Language Archive), and at the Linguistic Data Consortium (University of Pennsylvania).", "AwardID" -> "1500595", "Institution" -> Entity["NSFInstitution", "GettysburgCollege"], "Investigators" -> {Entity["NSFInvestigator", "JonathanAmith"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "7719", "Text" -> "DEL"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}, {"Code" -> "7298", "Text" -> "COLLABORATIVE RESEARCH"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500595&HistoricalAwards=false"], "KeywordTally" -> {{"speech", 8}, {"software", 7}, {"Mixtec", 4}, {"speakers", 4}, {"transcription", 4}, {"Yoloxochitl", 4}, {"create", 3}, {"language", 3}, {"native", 3}, {"project", 3}, {"transcribed", 3}, {"University", 3}, {"analysis", 2}, {"Archive", 2}, {"automatic", 2}, {"br/>

", 2}, {"collected", 2}, {"data", 2}, {"develop", 2}, {"endangered", 2}, {"materials", 2}, {"recognition", 2}, {"team", 2}, {"tool", 2}, {"train", 2}, {"training", 2}}|>, "1500601" -> <|"AwardTitle" -> "Gromov-Witten theory under extremal transitions and birational transformations", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[162000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "Gromov-Witten (GW) theory lies in the intersection of many exciting research areas in mathematics and physics. Roughly speaking it counts the number of curves meeting prescribed conditions in a geometric object called a variety. On the one hand, the theory itself has remarkable structures, both established and conjectural. Investigating these structures requires some new insights and technical tools from other areas. This provides a lot of interesting problems for classical subjects in mathematics. On the other hand, these new insights and technical tools help to discover deep relations and connections between existing mathematics and theoretical physics. This project will advance understanding in this active area of research. The project includes training of graduate students and postdocs, as well as international collaborations.\n\nThis research project lies on the intersection of algebraic geometry and mathematical physics. Specifically, it concerns the Gromov-Witten theory and variation of Hodge structures (VHS) on one side and birational geometry and mirror symmetry on the other. The main themes of the project are the study of GW theory of bundles and blowing-ups and the extended functoriality of GW and VHS under extremal transitions (also known as space-time topology change in the physics literature). The relations between the crepant transformation conjecture in GW theory and the Landau-Ginzburg / Calabi-Yau correspondence will also be studied.", "AwardID" -> "1500601", "Institution" -> Entity["NSFInstitution", "UniversityOfUtah"], "Investigators" -> {Entity["NSFInvestigator", "Yuan-PinLee"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500601&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 5}, {"GW", 4}, {"physics", 4}, {"project", 4}, {"mathematics", 3}, {"research", 3}, {"structures", 3}, {"areas", 2}, {"geometry", 2}, {"Gromov-Witten", 2}, {"hand", 2}, {"insights", 2}, {"intersection", 2}, {"lies", 2}, {"new", 2}, {"relations", 2}, {"technical", 2}, {"tools", 2}, {"VHS", 2}}|>, "1500604" -> <|"AwardTitle" -> "Engaging Male Colleagues as Advocates and Allies for the Advancement of Women Faculty", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2019, 8, 31}], "AwardAmount" -> Quantity[690638, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "11060000", "ProgramOfficer" -> "dana britton", "Abstract" -> "The PLAN-D funding track is designed to expand the application of proven-successful gender-equity initiatives for STEM faculty in a specific disciplinary area through networked adaptation of a specific program or initiative. Careful evaluation is expected to expand understanding of such initiatives in a disciplinary context. \n\nThe ADVOCATE FORWARD project is designed to improve the recruitment, retention, promotion, and sustainability of women faculty in engineering. North Dakota State University (NDSU), through its ADVANCE program, developed and implemented a signature program called Advocates & Allies (A&A) designed to improve gender equity through the direct and proactive engagement of male faculty. The program is comprised of two-parts: Advocates, senior male faculty who educate themselves about issues of gender [in]equality; and Allies, male faculty whom the Advocates train as proponents for gender equity in their departments. These men serve as change agents, committing to be active and vocal proponents of gender diversity and equality specifically in terms of increasing the number of female faculty, encouraging the hiring and promotion of female faculty in administrative positions, and ensuring the fair and equitable treatment of women within their units. NDSU has seen increased participation of women in all science and engineering faculty and academic administrative positions as a result of its ADVANCE project and the A&A program has been endorsed as a model program by the American Society for Engineering Education (ASEE). This project will test, refine, and grow the program into a national model. The core adaptation and implementation network partners include: NDSU; the Ohio State University; the Rochester Institute of Technology, the University of North Texas, and the University of Wyoming. This project has the potential to lead to the adoption of the A&A as a national model by ASEE following implementation and adaptation of the program by the network partners. This project will provide evidentiary support of how male advocates and allies can uniquely assist engineering programs in attracting and retaining more women faculty. In so doing, it will help grow a large cadre of faculty leaders trained as advocates and allies to advance the number of women (at all levels) in STEM.\n\nThis project will shed new light on the role, function, and utility of developing and implementing gendered-faculty advocate and ally groups in higher education as a means to advance efforts to support women faculty in STEM, particularly in engineering. Research on male faculty advocates and allies is virtually nonexistent. Most of the work in the area of ally groups in higher education has focused on male students or gay, lesbian, bisexual and transgendered support groups. The project goals include: (1) acquire new knowledge on the development and implementation of faculty advocate and ally groups in higher education as a means to improve climate for all faculty and women faculty in engineering in particular; (2) demonstrate the efficacy of advocates and allies in promoting gender equality and equity; and (3) become a fully established, self-sustaining locus of research, training, and support in proactively engaging men in gender equity efforts in schools of engineering across the country. The partner institutions offer a unique mix of characteristics: public/private, ADVANCE/non-ADVANCE, PhD/non-PhD granting, small/large, wide regional representation, and broad ethnic and gender diversity. These varied characteristics are essential to identifying and developing broadly applicable implementation models and training. This project focuses on engineering disciplines where there are a declining number of women studying and earning advanced degrees and more Ph.D. trained women are opting not to seek jobs in academia. \n\nThe NSF ADVANCE Partnerships for Learning and Adaptation Networks (PLAN) program track supports projects that promote the adaptation and implementation of previously effective ADVANCE programs in new contexts and the testing of innovative strategies to promote the participation, success, and advancement of women in STEM academic careers. PLAN projects also contribute to the knowledge base on gender equity in STEM academic careers.", "AwardID" -> "1500604", "Institution" -> Entity["NSFInstitution", "NorthDakotaStateUniversityFargo"], "Investigators" -> {Entity["NSFInvestigator", "CananBilen-Green"], Entity["NSFInvestigator", "RogerGreen"], Entity["NSFInvestigator", "ChristineMcGeorge"], Entity["NSFInvestigator", "ElizabethDell"], Entity["NSFInvestigator", "HazelMorrow-Jones"]}, "Directorate" -> "Direct For Education and Human Resources", "Division" -> "Division Of Human Resource Development", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500604&HistoricalAwards=false"], "KeywordTally" -> {{"faculty", 15}, {"women", 10}, {"program", 9}, {"gender", 8}, {"project", 8}, {"engineering", 7}, {"male", 6}, {"equity", 5}, {"implementation", 5}, {"adaptation", 4}, {"ADVANCE", 4}, {"advocates", 4}, {"allies", 4}, {"groups", 4}, {"STEM", 4}, {"support", 4}, {"University", 4}, {"&", 3}, {"academic", 3}, {"Advocates", 3}, {"ally", 3}, {"designed", 3}, {"education", 3}, {"higher", 3}, {"improve", 3}, {"model", 3}, {"NDSU", 3}, {"new", 3}, {"number", 3}, {"administrative", 2}, {"advance", 2}, {"advocate", 2}, {"Allies", 2}, {"area", 2}, {"ASEE", 2}, {"br/>

", 2}, {"careers", 2}, {"characteristics", 2}, {"developing", 2}, {"disciplinary", 2}, {"diversity", 2}, {"efforts", 2}, {"equality", 2}, {"expand", 2}, {"female", 2}, {"grow", 2}, {"include", 2}, {"initiatives", 2}, {"knowledge", 2}, {"large", 2}, {"means", 2}, {"men", 2}, {"national", 2}, {"network", 2}, {"North", 2}, {"participation", 2}, {"partners", 2}, {"PLAN", 2}, {"positions", 2}, {"programs", 2}, {"projects", 2}, {"promote", 2}, {"promotion", 2}, {"proponents", 2}, {"specific", 2}, {"State", 2}, {"track", 2}, {"trained", 2}, {"training", 2}}|>, "1500605" -> <|"AwardTitle" -> "Karuk (kyh) Archives and Accessibility Project", "AwardEffectiveDate" -> DateObject[{2015, 6, 15}], "AwardExpirationDate" -> DateObject[{2017, 11, 30}], "AwardAmount" -> Quantity[100000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Karuk is a language of the Karuk Tribe, a federally-recognized tribe situated on the middle course of the Klamath River in northwestern California. Karuk is well known for its complex accentual system such as the rules in English (PHOTOgraph versus photoGRAPHic), its unique patterns of word and sentence formation. Thus more data on this language will help with understanding more about its grammar.\n\nPI Susan Gehr of Humboldt University, along with a Karuk Language Program Coordinator and 20 community participants, will create an archival repository of Karuk materials, making them searchable and accessible in perpetuity. The materials to be archived include data from the Karuk Tribe's Language Program and materials donated by community members. These unique data will then enrich current knowledge of this highly endangered language.\n\nWhile there are just five elderly known fluent speakers of the Karuk language, there is an active community of Karuk people documenting the fluent speakers of Karuk and publishing Karuk texts, audio and video. Gehr will hold four workshops where she will share state-of-the-art techniques in archiving and preservation methodologies to community members with the view to supporting sustainable archiving practices in the community. The project will not only create infrastructure in the Karuk community, it also provided an example of how to do this with community. This project will also use best practices from the archival profession to produce a freely available collection guide for the Karuk language materials created and collected by the Karuk Tribe's Language Program.", "AwardID" -> "1500605", "Institution" -> Entity["NSFInstitution", "KarukTribe"], "Investigators" -> {Entity["NSFInvestigator", "SusanGehr"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500605&HistoricalAwards=false"], "KeywordTally" -> {{"Karuk", 13}, {"community", 7}, {"language", 4}, {"materials", 4}, {"data", 3}, {"Language", 3}, {"Program", 3}, {"archival", 2}, {"archiving", 2}, {"create", 2}, {"fluent", 2}, {"Gehr", 2}, {"known", 2}, {"members", 2}, {"practices", 2}, {"project", 2}, {"speakers", 2}, {"Tribe's", 2}, {"unique", 2}}|>, "1500607" -> <|"AwardTitle" -> "KUMU PDE Conference Proposal", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 3, 31}], "AwardAmount" -> Quantity[15500, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Victor Roytburd", "Abstract" -> "This award will provide support for participants, especially graduate students, junior researchers, women and mathematicians from under-represented groups in the sciences, to attend the regional conference \"KUMU Conference in PDE, Dynamical Systems and Applications\" to be held at the University of Kansas from April 18-19, 2015, co-organized by faculty from the University of Kansas (KU) and the University of Missouri (MU). Nearly all important physical phenomena are governed by fundamental laws and design principles that directly relate rates of change of some quantity to that of some other quantity. Indeed, given the initial conditions and the physical laws of motion one seeks to predict the future and reconstruct the past. This important observation naturally leads to the idea of a differential equation, thus providing the key to understanding many real-world problems. Differential equations are widely used as models in mathematical physics and have potential applications to many fields including Bose-Einstein condensates, fluid dynamics, pattern formation, gas dynamics and for modeling signals in optical communication networks. This conference will facilitate greater interaction between researchers in differential equations and its related fields from the area close to Kansas and Missouri. Planned as the first of a series of annual meetings, the conference will provide a venue for regional junior and established researchers, as well as graduate students to discuss the recent advances and challenges in their respective fields. In addition, young researchers will be given the opportunity to present their own work and to gain insights into this important subject through interactions with senior experts in the field. The conference website: https://www.math.ku.edu/conferences/2015/KUMUPDE/index.html\n\nComplex nonlinear systems abound in science and engineering, and their behavior is often modeled by systems of nonlinear partial differential equations (PDE). Any progress towards understanding the behavior of their solutions is of paramount importance for a variety of practical applications, including fluid flow, flame front propagation and fiber optical communication. Many PDE can be conveniently described as infinite dimensional dynamical systems, allowing for the use of tools and methodologies from dynamical systems theory to make qualitative and quantitative predictions about the solutions of these systems. Objects like invariant manifolds have been a great aid in understanding the behavior of finite-dimensional dynamical systems, but the connections between nonlinear PDE's and dynamical systems is still an area active current research. In the last few decades, collaborations between researchers in these fields, as well as with those working in their applications, have provided tremendous progress in our understanding of the dynamical behavior, stability and robustness of coherent structures in such nonlinear PDE. The main themes of this conference include (i) fluid dynamics, water waves and dispersive PDE's, (ii) existence, dynamics, and stability of nonlinear waves in dissipative systems, and (iii) dynamical systems and 2d-Navier Stokes equations.The techniques used to solve many challenging problems in these broad areas often combine ideas and methodologies from dynamical systems and partial differential equations together with probability theory, spectral and functional analysis, Evans functions, and geometric singular perturbation theory, to name a few.", "AwardID" -> "1500607", "Institution" -> Entity["NSFInstitution", "UniversityOfKansasCenterForResearchInc"], "Investigators" -> {Entity["NSFInvestigator", "MilenaStanislavova"], Entity["NSFInvestigator", "MathewJohnson"]}, "ProgramElements" -> {{"Code" -> "1266", "Text" -> "APPLIED MATHEMATICS"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500607&HistoricalAwards=false"], "KeywordTally" -> {{"systems", 10}, {"dynamical", 7}, {"conference", 5}, {"nonlinear", 5}, {"researchers", 5}, {"behavior", 4}, {"differential", 4}, {"dynamics", 4}, {"equations", 4}, {"fields", 4}, {"PDE", 4}, {"understanding", 4}, {"applications", 3}, {"fluid", 3}, {"important", 3}, {"Kansas", 3}, {"theory", 3}, {"University", 3}, {"area", 2}, {"communication", 2}, {"given", 2}, {"graduate", 2}, {"including", 2}, {"junior", 2}, {"laws", 2}, {"methodologies", 2}, {"Missouri", 2}, {"optical", 2}, {"partial", 2}, {"PDE's", 2}, {"physical", 2}, {"problems", 2}, {"progress", 2}, {"provide", 2}, {"quantity", 2}, {"regional", 2}, {"solutions", 2}, {"stability", 2}, {"students", 2}, {"used", 2}, {"waves", 2}}|>, "1500613" -> <|"AwardTitle" -> "Questions on Local Cohomology and Tight Closure Theory", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[219999, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "This project is concerned with several questions in commutative algebra. This is a field that studies solution sets of polynomial equations. Understanding solution sets of polynomial equations is of fundamental importance in many sciences, in engineering, and in other disciplines as well. Most of the questions that will be investigated deal with the nature of the solution sets: some are questions that have been unresolved for a number of years, but for which recent advances provide the likelihood of a solution; others arise naturally from new developments in the area. A number of projects are connected with local cohomology theory: this theory often provides the best answers to basic questions such as the least number of polynomials needed to define a solution set.\n\nThe projects on local cohomology theory include algorithmic aspects, as well as structural properties such as support and injective dimension. There is a special focus on local cohomology modules of polynomial rings and hypersurfaces over the integers: this stems from the fact that there is a canonical homomorphism from the integers to any ring, and this makes local cohomology modules over the integers, in a sense, universal; this viewpoint has proved useful in recent work of the PI and collaborators. The project will also investigate local cohomology over the integers. The research will further develop the connections of local cohomology with prime characteristic numerical invariants such as the F-pure threshold, and will study the composition series of local cohomology modules over rings of differential operators.", "AwardID" -> "1500613", "Institution" -> Entity["NSFInstitution", "UniversityOfUtah"], "Investigators" -> {Entity["NSFInvestigator", "AnuragSingh"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500613&HistoricalAwards=false"], "KeywordTally" -> {{"cohomology", 7}, {"local", 7}, {"solution", 5}, {"integers", 4}, {"questions", 4}, {"modules", 3}, {"number", 3}, {"polynomial", 3}, {"sets", 3}, {"theory", 3}, {"equations", 2}, {"project", 2}, {"projects", 2}, {"recent", 2}, {"rings", 2}}|>, "1500615" -> <|"AwardTitle" -> "Model Theory and Ergodic Theorems", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2018, 4, 30}], "AwardAmount" -> Quantity[170356, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "Ergodic theory is a branch of mathematics concerned with the behavior of dynamical systems when they are allowed to run over long time intervals. One of the fundamental results of ergodic theory is the Mean Ergodic Theorem of von Neumann (1932), which amounts to an abstract statement about the limiting average state of a conservative system. In this project we seek to apply concepts and techniques of model theory, a branch of mathematical logic, to establish results on ergodic averages and ergodic recurrence by reinterpreting and extending research results discovered in the decades following von Neumann. The model-theoretic viewpoint should help illuminate and potentially unveil connections between ergodic theory and other branches of mathematics.\n\nOne of the project's goals is casting recent results on convergence of multiple ergodic averages into a suitable model-theoretic framework that allows combining analytic arguments with the theory of types, forking calculus, and ordinal ranks. An important concept in the proposed research is a ranking of the complexity of \"polynomial actions\" of a group G on some measure space X, or rather of the induced (polynomial) actions of G on various topological spaces (say, of functions on X). This requires developing an abstract algebraic framework that extends Leibman's theory of polynomial mappings between groups. Ancillary anticipated products of the model-theoretic approach include results on metastable convergence (akin to a weak form of uniformity in situations in which uniform convergence is absent), on convergence of averages on ultraproducts of polynomial-ergodic systems, and on polynomial-ergodic actions of ordinal (transfinite) rank (generalized Leibman degree).Connections and applications to combinatorics, Ramsey theory, and number theory will also be studied.", "AwardID" -> "1500615", "Institution" -> Entity["NSFInstitution", "UniversityOfTexasAtSanAntonio"], "Investigators" -> {Entity["NSFInvestigator", "JoseIovino"], Entity["NSFInvestigator", "EduardoDuenez"]}, "ProgramElements" -> {{"Code" -> "1268", "Text" -> "FOUNDATIONS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500615&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 8}, {"ergodic", 5}, {"results", 5}, {"convergence", 4}, {"actions", 3}, {"averages", 3}, {"model-theoretic", 3}, {"polynomial", 3}, {"abstract", 2}, {"branch", 2}, {"Ergodic", 2}, {"framework", 2}, {"G", 2}, {"Neumann", 2}, {"ordinal", 2}, {"polynomial-ergodic", 2}, {"research", 2}, {"systems", 2}, {"von", 2}, {"X", 2}}|>, "1500620" -> <|"AwardTitle" -> "COLLBORATIVE RESEARCH: CREATING AN AUDIO-VISUAL CORPUS OF SCOTTISH GAIDHLIG TO PRESERVE AND INVESTIGATE LINGUISTIC DIVERSITY", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 11, 30}], "AwardAmount" -> Quantity[36928, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Joan Maling", "Abstract" -> "Scottish Gaelic, a Celtic language closely related to Irish and Welsh and more distantly to English, was once spoken across Scotland by most of the country's population. Today, however, Gaelic remains a community language only in the most remote regions of western Scotland. Gaelic speakers comprise about 1% of the Scottish population; the 2011 census found only 57,375 native speakers, compared to 250,000 a century earlier. This sharp decline makes the language's continued survival uncertain. \n\nScottish Gaelic is of immense interest because it possesses many rare linguistic features, including initial consonant mutation where a word-initial consonant can be changed depending on the function of that word in a clause. Scottish Gaelic also exhibits pre-aspirated consonants, and verb-initial sentence structure. In addition, the language offers remarkable examples of how knowledge systems particular to local geography and climate (land management, fishing techniques) are imbedded in the language. Should Scottish Gaelic become extinct, the global community -- not just Scotland -- will lose an irreplaceable cultural and scientific resource. \n\nThrough this two-year project, Professors Ian Clayton from the University of Nevada, Reno along with Andrew Carnie and Mike Hammond from the University of Arizona will create a corpus of linguistic interviews with 30 native Gaelic speakers. They will be assisted by native speaker Muriel Fisher, the recipient of the Linguistic Society of America's 2015 Excellence in Community Linguistics Award. The collection will contain more than twenty hours of high-quality audio-visual material, transcribed and translated and will include speech samples from speakers over range of ages, geographic origins, and professional backgrounds.\n\nThe collection will offer an invaluable tool to help linguists expand their scientific study of this language's rare features. In addition, the interviews will focus on traditional occupations, folklore, and oral history-- the kinds of knowledge and terminology most at risk as Gaelic declines. \n\nWhen complete, the corpus will be publically available through the Max Planck Institute's Language Archive, and the University of Arizona's Open Repository.", "AwardID" -> "1500620", "Institution" -> Entity["NSFInstitution", "BoardOfRegents,NSHE,OboUniversityOfNevada,Reno"], "Investigators" -> {Entity["NSFInvestigator", "IanClayton"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500620&HistoricalAwards=false"], "KeywordTally" -> {{"Gaelic", 8}, {"language", 4}, {"Scottish", 4}, {"speakers", 4}, {"native", 3}, {"Scotland", 3}, {"University", 3}, {"addition", 2}, {"br/>

", 2}, {"collection", 2}, {"community", 2}, {"consonant", 2}, {"corpus", 2}, {"features", 2}, {"interviews", 2}, {"knowledge", 2}, {"language's", 2}, {"linguistic", 2}, {"population", 2}, {"rare", 2}, {"scientific", 2}}|>, "1500630" -> <|"AwardTitle" -> "Continuation of Full-Scale Three Dimensional Numerical Experiments of High-Intensity Particle and Laser Beam Matter Interactions", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[440000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Vyacheslav S. Lukin", "Abstract" -> "Particle accelerators are ubiquitous in society as they are used in particle physics, materials science, structural biology, medicine, and transmutation of nuclear waste. In some cases these accelerators are more than a mile long and cost billions of dollars. If a new cheaper and more compact accelerator technology could be developed, it would transform our ability to use particle accelerators and enable their application to an even wider range of problems of scientific and societal benefit. This research will examine fundamental scientific questions aimed at developing compact particle accelerators based on plasma waves (these are waves moving in fully ionized gases) moving near the speed of light. It will also require generating state-of-the-art software that can be used on the nation's largest computers. The students and post-doctoral researchers trained under this grant will be part of the twenty first century work force in computational science and engineering as well as experts in plasma physics and accelerator physics.\n\nThis is an award to perform full-scale three-dimensional numerical experiments of high-intensity particle and laser beam-matter interactions to significantly advance the understanding of basic high-energy density science (HEDS) on ultra intense laser and particle beam plasma interactions. This understanding will aid in the quest to make plasma based accelerator stages for use in high energy physics colliders, next generation light sources, medicine, and homeland security. This work will continue to blend basic research with three-dimensional simulations, including full-scale particle-in-cell modeling of ongoing and planned experiments. High-fidelity full-scale modeling provides the means to extrapolate parameters into regimes that will not be accessible to experiments for years to come. During the past decade, a hierarchy of state-of-the-art PIC codes and data analysis tools for HEDS studies has been developed that not only include the necessary physics but also scale to more than 1,600,000 cores and can run on current many core hardware including GPUs and Intel Phi's. With this set of tools, the UCLA Simulation of Plasma Group is uniquely positioned to continue to make significant progress towards determining the feasibility of building a compact X-Ray Free Electron Laser (XFEL) in the next decade, and a future linear collider based on wakefield sections driven by lasers or particle beams.", "AwardID" -> "1500630", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-LosAngeles"], "Investigators" -> {Entity["NSFInvestigator", "WarrenMori"], Entity["NSFInvestigator", "FrankTsung"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500630&HistoricalAwards=false"], "KeywordTally" -> {{"particle", 6}, {"accelerators", 4}, {"physics", 4}, {"plasma", 4}, {"accelerator", 3}, {"based", 3}, {"compact", 3}, {"experiments", 3}, {"-scale", 3}, {"science", 3}, {"basic", 2}, {"continue", 2}, {"decade", 2}, {"developed", 2}, {"-dimensional", 2}, {"HEDS", 2}, {"including", 2}, {"interactions", 2}, {"laser", 2}, {"light", 2}, {"make", 2}, {"medicine", 2}, {"modeling", 2}, {"moving", 2}, {"research", 2}, {"scientific", 2}, {"state---art", 2}, {"tools", 2}, {"understanding", 2}, {"use", 2}, {"used", 2}, {"waves", 2}, {"work", 2}}|>, "1500644" -> <|"AwardTitle" -> "Representations of Real Lie Groups, Symmetry Breaking, and Automorphic Forms", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[95919, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "The investigator will continue long-term research into the study of symmetries and some of their applications. Symmetry is a mathematical concept with direct applications in other sciences such as chemistry, physics, biology, and engineering. The study of algebra, of which this research is a part, is in many ways the study of symmetries. This project aims to advance understanding of important algebraic structures, with potential applications to number theory and theoretical physics.\n\nThis research project is concerned with symmetry breaking, that is, obtaining representations of a smaller Lie group from the representations of a large reductive semi-simple Lie group. The representations of the large group are usually infinite dimensional, and the representations of smaller groups are related to quotients of the original representation of the large group. Symmetry breaking of representations is far from well understood, and so the constructions and the understanding of examples are very important. This research has applications to number theory and possibly to theoretical physics. Many of the techniques used in these constructions are analytic, and thus some new, interesting, and challenging problems in analysis arise and need to be solved.", "AwardID" -> "1500644", "Institution" -> Entity["NSFInstitution", "CornellUniversity"], "Investigators" -> {Entity["NSFInvestigator", "BirgitSpeh"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500644&HistoricalAwards=false"], "KeywordTally" -> {{"representations", 5}, {"applications", 4}, {"group", 4}, {"research", 4}, {"large", 3}, {"study", 3}, {"breaking", 2}, {"constructions", 2}, {"important", 2}, {"Lie", 2}, {"number", 2}, {"physics", 2}, {"project", 2}, {"smaller", 2}, {"symmetries", 2}, {"Symmetry", 2}, {"theoretical", 2}, {"theory", 2}, {"understanding", 2}}|>, "1500646" -> <|"AwardTitle" -> "Scattering theory on singular spaces", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[156916, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Linear and nonlinear wave equations model many phenomena, including electromagnetic and gravitational waves. Their study is central to at least two areas of mathematics: scattering theory and general relativity. This project focuses on the study of partial differential equations on singular spaces with an emphasis on the scattering theory of waves. The long-time behavior of wave equations on smooth spaces is well-understood in many regards, but the presence of singularities raises many unresolved problems. The singularities studied include boundaries, cone points, and large-scale structures \"at infinity.\" These projects are of interest to mathematicians and physicists working in partial differential equations, geometry, general relativity, and numerical analysis. The investigator intends to foster communication among researchers in these communities through collaboration and by organizing conferences in these fields.\n\nThis research will provide new insights into the long-time behavior of waves in novel contexts. Other than on perturbations of Euclidean and hyperbolic spaces, very little fine information is known about the long-time behavior of waves. Many facts that are known to hold for the linear wave equation in flat space are largely unknown when the underlying spacetime on which the evolution takes place is instead time-dependent or singular. The investigator will employ microlocal, or phase space, techniques to explore problems in these areas. In particular, the investigator will address problems concerning (1) wave decay on curved spacetimes such as those arising in general relativity, (2) wave maps, or nonlinear sigma models in the language of quantum field theory, on conic surfaces, and (3) boundary value problems for the Helmholtz equation arising in numerical analysis.", "AwardID" -> "1500646", "Institution" -> Entity["NSFInstitution", "TexasA&MUniversityMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "DeanBaskin"]}, "ProgramElements" -> {{"Code" -> "1265", "Text" -> "GEOMETRIC ANALYSIS"}, {"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500646&HistoricalAwards=false"], "KeywordTally" -> {{"wave", 5}, {"equations", 4}, {"problems", 4}, {"waves", 4}, {"behavior", 3}, {"general", 3}, {"investigator", 3}, {"long-time", 3}, {"relativity", 3}, {"spaces", 3}, {"theory", 3}, {"analysis", 2}, {"areas", 2}, {"arising", 2}, {"differential", 2}, {"equation", 2}, {"known", 2}, {"nonlinear", 2}, {"numerical", 2}, {"partial", 2}, {"scattering", 2}, {"singular", 2}, {"singularities", 2}, {"space", 2}, {"study", 2}}|>, "1500647" -> <|"AwardTitle" -> "Geometry and Topology of the Heisenberg Groups", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[132673, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "The Heisenberg group appeared for the first time in Herman Weyl's proof that the Schrodinger and the Heisenberg approaches to quantum mechanics are mathematically equivalent. However, the scope of applications of the Heisenberg groups goes far beyond quantum mechanics. The Heisenberg groups play an important role in many areas of mathematics and also in the mathematical biology in the development of a mathematical model of the visual cortex. Although the Heisenberg groups have been studied for several decades now, recent developments, leading to applications in new areas of pure and applied mathematics, provide new perspectives. This research project will advance this very active area of contemporary mathematics. The project will provide ample opportunity for graduate students and postdoctoral associates to be trained in this important area that bridges different fields of mathematics. Four graduate students and two postdoctoral associates will actively work on topics related to the project. \n\nThe research will lead to a development of the program introduced in a seminal work of M. Gromov and it will consist of several independent, but related tasks. Most of the tasks will be carried out as a joint projects of the PI with his graduate students, postdoctoral associates and other researchers from the US and Europe. The project will investigate the following problems. (1) Develop the theory of Lipschitz homotopy groups of the Heisenberg groups. Unlike the classical homotopy groups, the Lipschitz homotopy groups provide a deeper insight into the geometry of Holder, Lipschitz, and Sobolev mappings into the Heisenberg group. (2) Characterize the pairs of the Heisenberg groups that have the Lipschitz extension property. The Lipschitz extension property is very difficult to study, because the methods of the classical topology fail and a more quantitative and analytic methods are necessary. (3) Solve the problem of the Whitney extension for mappings into the Heisenberg group. While the Whitney extension theorem has proven to be one of the most influential results in analysis, the Heisenberg group provides a non-linear constraint that has not been investigated so far. (4) Develop the differential calculus of Holder continuous maps. This subject has recently and independently been discovered by many researchers working in different areas of mathematics and the goal of the PI is to find a unified approach which will lead to a simplification of some results of Gromov and will link the methods developed for the Heisenberg group with the geometric rigidity problems in convex integration. (5) Construct a counterexample to a conjecture of M. Gromov about Holder mappings into the Heisenberg group. Numerical examples show unexpected results, but they have to be verified rigorously. (6) Find a new characterization of mappings of bounded length distortion, a study motivated by unrectifiability of the Heisenberg group. Other topics under study in the project are: approximation of convex functions, boundedness of maximal functions in Sobolev spaces, homeomorphisms whose Jacobian changes sign, and continuity of Sobolev mappings with positive Jacobian.", "AwardID" -> "1500647", "Institution" -> Entity["NSFInstitution", "UniversityOfPittsburgh"], "Investigators" -> {Entity["NSFInvestigator", "PiotrHajlasz"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500647&HistoricalAwards=false"], "KeywordTally" -> {{"Heisenberg", 13}, {"groups", 8}, {"group", 7}, {"Lipschitz", 5}, {"mappings", 5}, {"mathematics", 5}, {"project", 5}, {"extension", 4}, {"areas", 3}, {"associates", 3}, {"graduate", 3}, {"Gromov", 3}, {"Holder", 3}, {"homotopy", 3}, {"methods", 3}, {"new", 3}, {"postdoctoral", 3}, {"provide", 3}, {"results", 3}, {"Sobolev", 3}, {"students", 3}, {"study", 3}, {"applications", 2}, {"area", 2}, {"classical", 2}, {"convex", 2}, {"Develop", 2}, {"development", 2}, {"different", 2}, {"far", 2}, {"functions", 2}, {"important", 2}, {"Jacobian", 2}, {"lead", 2}, {"M", 2}, {"mathematical", 2}, {"mechanics", 2}, {"PI", 2}, {"problems", 2}, {"property", 2}, {"quantum", 2}, {"related", 2}, {"research", 2}, {"researchers", 2}, {"tasks", 2}, {"topics", 2}, {"Whitney", 2}, {"work", 2}}|>, "1500652" -> <|"AwardTitle" -> "The Boot Camp for the 2015 Algebraic Geometry Summer Research Institute", "AwardEffectiveDate" -> DateObject[{2015, 2, 15}], "AwardExpirationDate" -> DateObject[{2016, 1, 31}], "AwardAmount" -> Quantity[49900, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "This award supports the participation of graduate students and postdoctoral researchers in the \"Boot Camp\" preceding the American Mathematical Society (AMS) Summer Institute in Algebraic Geometry on July 6-10, 2015 at the University of Utah, Salt Lake City. The algebraic geometry community has developed the now longstanding tradition of running an institute every ten years with the purpose of convening a majority of practitioners in the world to overview the developments of the past decade and to outline the most pressing and far-reaching problems for the next. The next AMS Summer Institute in Algebraic Geometry will take place at the University of Utah, Salt Lake City, on July 13-31, 2015. Increasingly, algebraic geometry has become so diverse and technically demanding that it is daunting for graduate students and postdocs to master the techniques and wide range of activity that occurs in the field beyond their immediate areas of study. It has thus become imperative to run a \"boot camp\" in the week preceding the institute designed exclusively for advanced graduate students and postdoctoral researchers. The purpose of the boot camp is threefold:\n1) To familiarize the participants with a broad range of developments in algebraic geometry in an informal setting, thus increasing their ability to follow discussions and participate at the institute.\n2) To introduce young algebraic geometers to their peers and the previous generation of experts in order to increase collaborations and form a support group for young researchers.\n3) To introduce young researchers to new techniques and questions in order to make them more effective researchers.\n\nThe boot camp will focus on several subjects in algebraic geometry that have seen significant advances in the last decade, including birational geometry, Bridgeland stability, the Hassett-Keel program, p-adic Hodge theory, Shimura varieties, perfectoid spaces, the tautological ring of the moduli spaces of curves, Boij-Soderbeg theory, and singularities in characteristic p. The choices of topics are results of coordination with the organizers of the AMS Summer Institute in Algebraic Geometry. The boot camp will have wide-ranging broader impacts as it will introduce the most dynamic and brightest young algebraic geometry graduate students and postdocs to each other. It is expected that many new collaborations will result from this interaction. In addition to the scientific benefits, young researchers will form a support network of their peers, which can significantly improve retention and success in the STEM disciplines. More details about the boot camp can be found at its website: http://www.math.utah.edu/~defernex/Bootcamp2015/home.html.", "AwardID" -> "1500652", "Institution" -> Entity["NSFInstitution", "UniversityOfGeorgiaResearchFoundationInc"], "Investigators" -> {Entity["NSFInvestigator", "AngelaGibney"], Entity["NSFInvestigator", "TommasoDeFernex"], Entity["NSFInvestigator", "MaxLieblich"], Entity["NSFInvestigator", "IzzetCoskun"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500652&HistoricalAwards=false"], "KeywordTally" -> {{"algebraic", 6}, {"geometry", 6}, {"boot", 5}, {"camp", 5}, {"young", 5}, {"graduate", 4}, {"researchers", 4}, {"students", 4}, {"Algebraic", 3}, {"AMS", 3}, {"Geometry", 3}, {"Institute", 3}, {"introduce", 3}, {"Summer", 3}, {"2015", 2}, {"City", 2}, {"collaborations", 2}, {"decade", 2}, {"developments", 2}, {"form", 2}, {"institute", 2}, {"July", 2}, {"Lake", 2}, {"new", 2}, {"order", 2}, {"peers", 2}, {"postdocs", 2}, {"postdoctoral", 2}, {"preceding", 2}, {"purpose", 2}, {"range", 2}, {"Salt", 2}, {"spaces", 2}, {"support", 2}, {"techniques", 2}, {"theory", 2}, {"University", 2}, {"Utah", 2}}|>, "1500654" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Identifying the pollen tube chemoattractant regulating gamete recognition in the wild tomato clade (Solanum sect. Lycopersicon)", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2016, 11, 30}], "AwardAmount" -> Quantity[20129, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010207", "ProgramOfficer" -> "George W. Gilchrist", "Abstract" -> "This study aims to understand gamete recognition (chemical cues used by male and female gametes to recognize and attract each other) as a mechanism of sexual reproduction, and how it acts to prevent reproductive events between different species. This work uses the domesticated tomato and its twelve diverse wild species relatives, which vary in many reproductive and functional traits. The project will first identify the chemical signal derived from the female gamete that attracts the male gamete within species. Second, it will characterize variation in this signal across species and connect this variation to previously observed reduced gamete attraction between species. In addition to understanding molecular mechanisms of normal and attenuated reproductive function, these data could aid in overcoming breeding barriers between domesticated tomato and its genetically diverse wild relatives. This project will include research by undergraduates from underrepresented groups and potential insights of agricultural importance for crop breeding. \n\nTo identify the female gamete-derived chemoattractant and its specific tissue of origin, this project will use high depth nucleotide sequencing technologies (RNA-seq) for tissue specific expression analysis. It will assess molecular divergence of this signaling protein via variation in sequence and/or expression across 13 closely related species. These combined approaches will explicitly link patterns of molecular expression and DNA variation to functional divergence in reproductive behaviors. Although many studies have demonstrated that species show reduced sexual compatibility, the underlying molecular mechanisms are generally unknown. Together, this research will provide an unprecedented opportunity to examine the patterns and consequences of evolutionary changes in a reproductive molecule, including for the development of new species.", "AwardID" -> "1500654", "Institution" -> Entity["NSFInstitution", "IndianaUniversity"], "Investigators" -> {Entity["NSFInvestigator", "CathleenJewell"], Entity["NSFInvestigator", "LeonieMoyle"]}, "ProgramElements" -> {{"Code" -> "7378", "Text" -> "EVOLUTIONARY GENETICS"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500654&HistoricalAwards=false"], "KeywordTally" -> {{"species", 8}, {"reproductive", 5}, {"gamete", 4}, {"molecular", 4}, {"variation", 4}, {"expression", 3}, {"female", 3}, {"project", 3}, {"breeding", 2}, {"chemical", 2}, {"divergence", 2}, {"diverse", 2}, {"domesticated", 2}, {"functional", 2}, {"identify", 2}, {"male", 2}, {"mechanisms", 2}, {"patterns", 2}, {"reduced", 2}, {"relatives", 2}, {"research", 2}, {"sexual", 2}, {"signal", 2}, {"specific", 2}, {"tissue", 2}, {"tomato", 2}, {"wild", 2}}|>, "1500659" -> <|"AwardTitle" -> "Testing the Community Partnership Model through Lokono Language Documentation", "AwardEffectiveDate" -> DateObject[{2015, 7, 15}], "AwardExpirationDate" -> DateObject[{2017, 9, 30}], "AwardAmount" -> Quantity[115228, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Broadening the participation of underrepresented groups in science can have transformative methodological consequences. That is the hypothesis that Racquel Sapien Yamada of the University of Oklahoma (Norman) will test by implementing a new collaborative fieldwork model which extends the notion of community-inclusive field research by facilitating the documentation of one endangered language (Lokono) by native and heritage speakers of another (Kari'nja).\n\nKari'nja and Lokono (Arawak-arw) speakers live side-by-side in the Konomerume village of Suriname. They often intermarry. Data on Lokono and Karinja will elucidate the processes of language contact evidenced between these two languages. The data will also help the place of Lokono (Arawakan family) and Kari'nja (Cariban family) within their respective language families. Yamada and her team will document, analyze, and describe aspects of Lokono to further investigate these issues.\n\nThis project is at the forefront of a greater movement to encourage members of endangered language communities to play more active roles in research that affects them. The project team will provide training to build local infrastructure for future documentation. A graduate student from the University of Oklahoma will receive field research and international experience through participation in the project.\n\nThe project is supported by co-funds from the National Science Foundation's International Science and Engineering Office.", "AwardID" -> "1500659", "Institution" -> Entity["NSFInstitution", "UniversityOfOklahomaNormanCampus"], "Investigators" -> {Entity["NSFInvestigator", "Racquel-MariaYamada"]}, "ProgramElements" -> {{"Code" -> "7298", "Text" -> "COLLABORATIVE RESEARCH"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> "5926", "Text" -> "LATIN AMERICA, SDC"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500659&HistoricalAwards=false"], "KeywordTally" -> {{"Lokono", 5}, {"language", 4}, {"project", 3}, {"research", 3}, {"documentation", 2}, {"endangered", 2}, {"family", 2}, {"field", 2}, {"Oklahoma", 2}, {"participation", 2}, {"Science", 2}, {"speakers", 2}, {"team", 2}, {"University", 2}, {"Yamada", 2}}|>, "1500662" -> <|"AwardTitle" -> "2015 Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[23408, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "The Second Rocky Mountain-Great Plains Graduate Research Workshop in Combinatorics (GRWC), which will be held in Ames, IA during June 1-12, 2015, will involve approximately 35 graduate students, 6 postdoctoral researchers, and more than a dozen faculty members in an intense two-week collaborative research experience. Participants will work to solve important, relevant problems from graph theory, enumeration, combinatorial matrix theory, finite geometry, and other modern sub-disciplines of combinatorics. Students will prepare open problems prior to the workshop under the guidance of faculty mentors from the organizing committee, which consists of faculty from Iowa State University, the University of Colorado Denver, the University of Denver, the University of Nebraska Lincoln, and the University of Wyoming. These problems, presented at the workshop by their proposers or hosted on the workshop's secure problem wiki, will be worked on by small groups of participating students, postdocs, and faculty. For more information about the GRWC, including a detailed description of the workshop format, please see the workshop website at http://sites.google.com/site/rmgpgrwc \n\nThe goal of the collaborations at the heart of the GRWC is to produce high-quality, publishable research on a variety of topics. Another longer-term goal of the workshop is to help student participants expand their professional research networks. A strong research network is often a crucial part of building a generative and sustainable research program, and establishing these connections at an early career stage can have a long-term positive effect on the quality, impact, and depth of a professional's research portfolio. Participation in the GRWC will allow students to cultivate a large professional network of peers from the combinatorics community with whom they will be able to interact and collaborate throughout their careers. The GRWC will also offer professional development workshops to help students and postdocs prepare for job searches and future careers in academia, industry, or government. This award supports students and postdoctoral researchers only; faculty support is provided by the organizing institutions.", "AwardID" -> "1500662", "Institution" -> Entity["NSFInstitution", "IowaStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "LeslieHogben"], Entity["NSFInvestigator", "PaulHorn"], Entity["NSFInvestigator", "MichaelFerrara"], Entity["NSFInvestigator", "TyrrellMcAllister"], Entity["NSFInvestigator", "DerrickStolee"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}, {"Code" -> "1260", "Text" -> "INFRASTRUCTURE PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500662&HistoricalAwards=false"], "KeywordTally" -> {{"research", 6}, {"faculty", 5}, {"GRWC", 5}, {"students", 5}, {"University", 5}, {"workshop", 5}, {"problems", 3}, {"professional", 3}, {"careers", 2}, {"combinatorics", 2}, {"Denver", 2}, {"goal", 2}, {"help", 2}, {"network", 2}, {"organizing", 2}, {"postdocs", 2}, {"postdoctoral", 2}, {"prepare", 2}, {"researchers", 2}, {"theory", 2}}|>, "1500667" -> <|"AwardTitle" -> "Defense Information Systems Agency (DISA)", "AwardEffectiveDate" -> DateObject[{2014, 10, 15}], "AwardExpirationDate" -> DateObject[{2018, 9, 30}], "AwardAmount" -> Quantity[3786443, "USDollars"], "AwardInstrument" -> "Contract Interagency Agreement", "OrganizationCode" -> "06090200", "ProgramOfficer" -> "Patrick D. Smith", "Abstract" -> Missing["NotAvailable"], "AwardID" -> "1500667", "Institution" -> Entity["NSFInstitution", "DefenseInformationSystemsAgency"], "Investigators" -> {Entity["NSFInvestigator", "LawrenceMachabee"]}, "ProgramElements" -> {{"Code" -> "5146", "Text" -> "ANTARCTIC LOGISTICS SUPPORT"}, {"Code" -> "5115", "Text" -> "Antarctic Astrophys&Geosp Sci"}, {"Code" -> "5111", "Text" -> "ANTARCTIC ORGANISMS & ECOSYST"}, {"Code" -> "5116", "Text" -> "ANTARCTIC GLACIOLOGY"}, {"Code" -> "5113", "Text" -> "ANTARCTIC OCEAN & ATMOSPH SCI"}, {"Code" -> "038F", "Text" -> "OCEAN OBSERVATORIES INIT O&M"}, {"Code" -> "1680", "Text" -> "OCEAN TECH & INTERDISC COORDIN"}, {"Code" -> "7112", "Text" -> "SAGE"}, {"Code" -> "5292", "Text" -> "ANTARCTIC INTEGRATED SYS SCI"}, {"Code" -> "5112", "Text" -> "ANTARCTIC EARTH SCIENCES"}, {"Code" -> "5205", "Text" -> "ARCTIC RESRCH SUPPRT & LOGISTI"}, {"Code" -> "037F", "Text" -> "OCEAN OBSERVATORIES INITIATIVE"}, {"Code" -> "5140", "Text" -> "OPERATIONS SUPPORT PROGRAM"}}, "Directorate" -> "Directorate For Geosciences", "Division" -> "Division Of Polar Programs", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500667&HistoricalAwards=false"], "KeywordTally" -> Missing["NotAvailable"]|>, "1500670" -> <|"AwardTitle" -> "Dynamics with a combinatorial flavor", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[120000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "A collection of objects whose changes are governed by a deterministic, time-independent update rule is called a dynamical system. Many dynamical systems are too complicated to be understood locally, but nonetheless we can predict global properties of the long term behavior of these systems. The overall goal of this project is to use the properties of certain dynamical systems to answer questions motivated by problems in combinatorics and computer science, and to obtain a deeper understanding of the connections among such diverse fields. The research component of the project will be supplemented by mentoring, advising, conference organization and giving lectures on mathematics for a general audience. \n\nSpecifically, the investigator plans building on past results in multiple recurrence and convergence, further understanding the connections to nilpotent groups and the dynamical systems that can be defined on their homogeneous spaces (nilsystems). Such systems play a key role in understanding the limiting behavior of multiple ergodic averages and the PI proposes research to extend our knowledge of their role. The PI proposes building on past results concerning symbolic and topological dynamics to further understand relations between complexity, periodicity, and automorphism groups of shift systems. While most of the problems proposed are within dynamics, the research has strong relations to problems in combinatorics, number theory, and computer science. The PI will continue to explore these deep links, developing applications to these other areas and making use of recent advances in these other areas to address problems within dynamics.", "AwardID" -> "1500670", "Institution" -> Entity["NSFInstitution", "NorthwesternUniversity"], "Investigators" -> {Entity["NSFInvestigator", "BrynaKra"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500670&HistoricalAwards=false"], "KeywordTally" -> {{"systems", 6}, {"dynamical", 4}, {"problems", 4}, {"dynamics", 3}, {"PI", 3}, {"research", 3}, {"understanding", 3}, {"areas", 2}, {"behavior", 2}, {"building", 2}, {"combinatorics", 2}, {"computer", 2}, {"connections", 2}, {"groups", 2}, {"multiple", 2}, {"past", 2}, {"project", 2}, {"properties", 2}, {"proposes", 2}, {"relations", 2}, {"results", 2}, {"role", 2}, {"science", 2}, {"use", 2}}|>, "1500671" -> <|"AwardTitle" -> "Applications of Model Theory to Extremal Combinatorics and Compactifications of G-spaces", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[89999, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "Model theory, a branch of mathematical logic, studies general properties of mathematical structures. Work in model theory often answers questions in other areas of mathematics. In the recent years there have been exciting new developments in applications of model theory to combinatorics and analysis. This project advances research on definable topological groups and their actions, and also on combinatorial questions in the context of distal theories. \n\nThis research project builds upon the investigator's previous work on definable group actions and combinatorial properties of theories without independence properties. This project undertakes a systematic study of definable compactifications of group actions, and extremal combinatorics in the not-independence-property (NIP) setting. More specifically, the project studies extremal combinatorics in distal theories and the Erdos-Hajnal conjecture for graphs definable in NIP theories. The project will also investigate growth rates of Ramsey functions in o-minimal and other tame theories, and will develop a model theoretic framework for compactifications of continuous group actions, in particular Riemannian symmetric spaces.", "AwardID" -> "1500671", "Institution" -> Entity["NSFInstitution", "UniversityOfNotreDame"], "Investigators" -> {Entity["NSFInvestigator", "SergeiStarchenko"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500671&HistoricalAwards=false"], "KeywordTally" -> {{"project", 5}, {"theories", 5}, {"actions", 4}, {"definable", 4}, {"combinatorics", 3}, {"group", 3}, {"model", 3}, {"properties", 3}, {"theory", 3}, {"combinatorial", 2}, {"compactifications", 2}, {"distal", 2}, {"extremal", 2}, {"mathematical", 2}, {"NIP", 2}, {"questions", 2}, {"research", 2}, {"studies", 2}}|>, "1500674" -> <|"AwardTitle" -> "Documenting Warm Springs Ichishkiin, an endangered language of Oregon", "AwardEffectiveDate" -> DateObject[{2016, 4, 15}], "AwardExpirationDate" -> DateObject[{2019, 9, 30}], "AwardAmount" -> Quantity[159742, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "The essential elements that constitute the minimal scientific documentation of a language include a reference grammar, a dictionary, and transcribed narratives with translations and linguistic analysis. Contemporary digital tools in language documentation allow the integration of the building blocks, so that a linguistic database might use the dictionary to translate the narratives, use the narratives to add words to the dictionary. Electronic databases structure a set of data, in this case language material, and they facilitate searches for information by allowing various keywords or categories to be used. These kinds of digital documentation tools produce very rich databases, with sound files, photographs, grammar information, and entire stories, all which are possible data that can be entered and tagged. This project will employ digital language documentation tools to process and analyze materials in an endangered Native American language, Warm Springs Ichishkiin (also known as Sahaptin). The Native American Languages Act, passed by the U.S. Congress in 1990, enacted into policy the recognition of the unique status and importance of Native American languages. By using digital tools to assist in the analysis of Native American languages, this project will increase access to linguistic and cultural materials, traditional cultural knowledge, and produce and disseminate a grammar and a dictionary. Broader impacts include training workshops for tribal citizens, and a best practices collaboration among the community elders, the tribal language program and academics. This will broaden participation by increasing the number of Native American citizen scientists as Confederated Tribes of Warm Springs community members are trained in the scientific methods of linguistic documentation and apply them to their own language.\n\nThis project will document and analyze discourse, morphosyntax and semantics in the Warm Springs Ichishkiin language which is spoken on the Warm Springs Reservation in the volcanic valleys of the Cascade Mountains in Oregon, USA. With no more than 50 elder speakers remaining, the translation and interpretation tasks are urgent. The collaborative team will include the Confederated Tribes of Warm Springs Language Program and community, joined by linguists from Portland State University and the Northwest Indian Language Institute of the University of Oregon. Valerie Switzler of the Confederated Tribes of Warm Springs, Nariyo Kono of Portland State University and Joana Jansen of the University of Oregon will work with digitized copies of reel-to-reel and cassette tapes as well as newly collected audio and video materials. The researchers will create transcriptions and translations that will contribute to a deeper level of understanding of lexical and grammatical features of Ichishkiin. A database, updated dictionary and updated grammar will result. Scientific interest in the language includes verbal morphology, referent tracking systems and metrical patterns, as these appear to differ in related varieties. Investigations will lead to a greater understanding of the relationships within the larger Sahaptian family, including Nez Perce and other of Ichishkiin varieties. This project will also provide a pathway to mobilizing the data and findings in the community's language programs, and in the continued maintenance of the Warm Springs Ichishkiin language within the tribe.", "AwardID" -> "1500674", "Institution" -> Entity["NSFInstitution", "UniversityOfOregonEugene"], "Investigators" -> {Entity["NSFInvestigator", "JoanaJansen"], Entity["NSFInvestigator", "NariyoKono"], Entity["NSFInvestigator", "ValerieSwitzler"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500674&HistoricalAwards=false"], "KeywordTally" -> {{"language", 10}, {"Springs", 7}, {"Warm", 7}, {"American", 5}, {"dictionary", 5}, {"documentation", 5}, {"Ichishkiin", 5}, {"Native", 5}, {"digital", 4}, {"grammar", 4}, {"linguistic", 4}, {"project", 4}, {"tools", 4}, {"University", 4}, {"community", 3}, {"Confederated", 3}, {"data", 3}, {"include", 3}, {"materials", 3}, {"narratives", 3}, {"Oregon", 3}, {"Tribes", 3}, {"analysis", 2}, {"analyze", 2}, {"cultural", 2}, {"database", 2}, {"databases", 2}, {"information", 2}, {"Language", 2}, {"languages", 2}, {"Portland", 2}, {"produce", 2}, {"scientific", 2}, {"State", 2}, {"translations", 2}, {"tribal", 2}, {"understanding", 2}, {"updated", 2}, {"use", 2}, {"varieties", 2}}|>, "1500675" -> <|"AwardTitle" -> "Completeness problems, Carleson measures, and spaces of analytic functions", "AwardEffectiveDate" -> DateObject[{2015, 2, 1}], "AwardExpirationDate" -> DateObject[{2016, 1, 31}], "AwardAmount" -> Quantity[16078, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This award provides funding to help defray the expenses of U.S. participants in the international conference \"Completeness Problems, Carleson Measures, and Spaces of Analytic Functions\" that will be held July 6-10, 2015, at the Mittag-Leffler Institute in Djursholm, Sweden. This conference brings together a host of international authorities to explore topics that lie at the interface of harmonic analysis, complex analysis, and operator theory. The topics of the conference are of wide interest in several areas of mathematics and also have impact outside of mathematics. In particular, the completeness problems are related to solution of Sturm-Liouville and Schroedinger differential equations, of importance in mathematical physics, and model spaces have important applications in control theory, of interest in engineering.\n\nThe conference will focus on recent progress in function theory, model spaces, completeness problems, and Carleson measures; in particular, on two recent stunning developments in the area: Poltoratski's research into the completeness of eigenfunction solutions to certain differential equations and Lacey's work on Carleson measures. Bringing together seasoned researchers and promising young mathematicians to address research challenges in this area is likely to lead to important new questions, inspire further research and new collaborations, and lead to new breakthroughs. The conference program provides ample opportunity for graduate students, postdocs, and other young scientists to present their work. \n\nConference web site: http://www.mittag-leffler.se/?q=150629", "AwardID" -> "1500675", "Institution" -> Entity["NSFInstitution", "BaylorUniversity"], "Investigators" -> {Entity["NSFInvestigator", "ConstanzeLiaw"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500675&HistoricalAwards=false"], "KeywordTally" -> {{"conference", 5}, {"Carleson", 3}, {"completeness", 3}, {"new", 3}, {"research", 3}, {"theory", 3}, {"analysis", 2}, {"area", 2}, {"differential", 2}, {"equations", 2}, {"important", 2}, {"international", 2}, {"lead", 2}, {"mathematics", 2}, {"measures", 2}, {"model", 2}, {"particular", 2}, {"problems", 2}, {"provides", 2}, {"recent", 2}, {"spaces", 2}, {"topics", 2}, {"work", 2}, {"young", 2}}|>, "1500677" -> <|"AwardTitle" -> "Dynamics on homogeneous spaces and Moduli spaces", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[129494, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "Dynamical systems is the study of the evolution of systems which are changing over time. As a concrete example one can consider the trajectory of a ball on an ideal table. The table is frictionless and the angle of incidence equals the angle of reflection. A classical mathematical problem is to study the trajectories of a ball when the sides of the table form a polygon - not necessarily a rectangle. There can be different types of trajectories. Some trajectories can be periodic and some can be dense on the table. This simple problem is notoriously difficult. It is very difficult to solve the problem for a particular table, unless it is of a special shape; for example, a rectangle or an equilateral triangle. This leads to the study of families of tables that have similarities. You could for instance, study the family of tables with five sides. Taking the family of tables as a new space it is possible to define a new flow on this space. This point of view turns out to have important consequences. For example, we may now be able to say what happens on \"most\" tables. This proposal studies dynamical systems by taking a similar point of view.\n\nWe mainly seek rigidity results where rather weak initial data about an object yields an almost complete classification of the object. The following will be the main objectives: \n(i) Employing a dynamical approach to study problems in number theory and geometry has proven rather fruitful. However, this approach is often noneffective. \nWe will seek effectivization of the rigidity phenomena for the action of groups generated by unipotent subgroups on homogeneous spaces; these rigidity results have served as one of the main tools in the aforementioned applications. \n(ii) There is an action of the group of nonsingular, real, two by two matrices on the moduli space of a compact Riemann surface; this is closely related to the asymptotic of the number of periodic trajectories on rational polygonal tables. \nThis proposal seeks generalizations of the recent exciting developments which proved certain rigidity results for this action. \n(iii) We attempt to investigate dynamics on homogeneous spaces with infinite volume, and on homogeneous spaces arising from local fields of positive characteristic. There are various geometric and number theoretical applications which motivate the study of these spaces.", "AwardID" -> "1500677", "Institution" -> Entity["NSFInstitution", "UniversityOfTexasAtAustin"], "Investigators" -> {Entity["NSFInvestigator", "AmirMohammadi"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500677&HistoricalAwards=false"], "KeywordTally" -> {{"study", 6}, {"table", 5}, {"tables", 5}, {"rigidity", 4}, {"spaces", 4}, {"trajectories", 4}, {"action", 3}, {"example", 3}, {"homogeneous", 3}, {"number", 3}, {"problem", 3}, {"results", 3}, {"space", 3}, {"systems", 3}, {"angle", 2}, {"applications", 2}, {"approach", 2}, {"ball", 2}, {"br", 2}, {"difficult", 2}, {"dynamical", 2}, {"family", 2}, {"main", 2}, {"new", 2}, {"object", 2}, {"periodic", 2}, {"point", 2}, {"proposal", 2}, {"rectangle", 2}, {"seek", 2}, {"sides", 2}}|>, "1500685" -> <|"AwardTitle" -> "Topics in Symbolic Dynamics", "AwardEffectiveDate" -> DateObject[{2015, 6, 15}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[161416, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "In the current project, the PI will explore several questions and open problems in the area of symbolic dynamics. Dynamics is the study of closed systems whose elements evolve over time according to deterministic rules; some examples include planetary motion, or a particle's movement inside a box. Symbolic dynamics is the study of dynamics where the elements in question are infinite sequences of symbols, and the evolution over time comes from horizontally shifting the sequence. Symbolic dynamics was introduced as a tool for studying more complicated dynamical systems, but has become a fundamental area in its own right, with applications and connections ranging from computer science (e.g. data storage in binary) to statistical physics (e.g. the Ising model for magnetism). A current area of high activity is multidimensional symbolic dynamics, in which one considers not sequences, but multidimensional arrays of symbols, which can be shifted in any direction. Though the core definitions and ideas remain the same, there are remarkable changes that occur for multiple dimensions; many questions that were easy to answer in one dimension become quite difficult, and classes of systems whose behavior was relatively simple in one dimension can exhibit strange and complex behaviors.\n\nThe research supported by this grant will treat a variety of problems in symbolic dynamics, ranging from the more classical one-dimensional case to the less well-understood multidimensional case. A common thread throughout is the use of ideas, techniques, and viewpoints from other areas, including probability theory, statistical physics, and percolation theory, to attack fundamental problems. The two projects on one-dimensional symbolic dynamics propose new directions of research about the classical notions of follower sets and the specification property respectively. The first multidimensional project proposes a new method for the efficient approximation of entropies of multidimensional shifts of finite type (SFT) which, unlike existing techniques, can be used on systems with multiple measures of maximal entropy. The final project will extend recent work by the PI and Kevin McGoff on random multidimensional SFTs, in which a probabilistic framework was defined where a \"typically\" chosen multidimensional SFT does not exhibit the worst pathological behaviors of the class; we now plan to use this framework to prove multidimensional probabilistic versions of some classical one-dimensional results. All work will be disseminated through publications in peer-reviewed journals, conference presentations, and the author's continued collaboration with young researchers, including his two Ph.D. students.", "AwardID" -> "1500685", "Institution" -> Entity["NSFInstitution", "UniversityOfDenver"], "Investigators" -> {Entity["NSFInvestigator", "RonaldPavlov"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500685&HistoricalAwards=false"], "KeywordTally" -> {{"multidimensional", 8}, {"dynamics", 7}, {"symbolic", 4}, {"systems", 4}, {"area", 3}, {"classical", 3}, {"-dimensional", 3}, {"problems", 3}, {"project", 3}, {"case", 2}, {"current", 2}, {"dimension", 2}, {"e.g.", 2}, {"elements", 2}, {"exhibit", 2}, {"framework", 2}, {"fundamental", 2}, {"ideas", 2}, {"including", 2}, {"multiple", 2}, {"new", 2}, {"physics", 2}, {"PI", 2}, {"probabilistic", 2}, {"questions", 2}, {"ranging", 2}, {"research", 2}, {"sequences", 2}, {"SFT", 2}, {"statistical", 2}, {"study", 2}, {"Symbolic", 2}, {"symbols", 2}, {"techniques", 2}, {"theory", 2}, {"time", 2}, {"use", 2}, {"work", 2}}|>, "1500691" -> <|"AwardTitle" -> "Algebraic combinatorics: symmetric orbit closures and Schubert calculus", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[220428, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "The goal of this project is to construct combinatorial models. Combinatorial problems arise in many areas of mathematics and have applications that include optimization, computer science, and statistical physics. The central focus of this research is the study of polynomial equations that appear at the interface of the study of discrete mathematics, geometry, and symmetries. A key component of this project will be the training of students (high school, undergraduate, and graduate) and postdoctoral faculty. Thereby, we wish to help strengthen the STEM education and research infrastructure in the United States.\n\nEarlier work of the investigator has led to precise connections of equivariant cohomology with spectra of Hermitian matrices, combinatorial commutative algebra with Kazhdan-Lusztig polynomials, combinatorial K-theory with longest increasing subsequences in random words, and partition combinatorics with bibliometric indicators. Such examples motivate finding broader and more unified combinatorial laws, which is the goal of this project. This research will both deepen our understanding of such connections and help discover novel relationships.", "AwardID" -> "1500691", "Institution" -> Entity["NSFInstitution", "UniversityOfIllinoisAtUrbana-Champaign"], "Investigators" -> {Entity["NSFInvestigator", "AlexanderYong"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}, {"Code" -> "7970", "Text" -> "Combinatorics"}}, "ProgramReferences" -> {{"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500691&HistoricalAwards=false"], "KeywordTally" -> {{"combinatorial", 4}, {"project", 3}, {"research", 3}, {"connections", 2}, {"goal", 2}, {"help", 2}, {"mathematics", 2}, {"study", 2}}|>, "1500692" -> <|"AwardTitle" -> "Workshop on partial differential equations and several complex variables", "AwardEffectiveDate" -> DateObject[{2015, 1, 15}], "AwardExpirationDate" -> DateObject[{2015, 12, 31}], "AwardAmount" -> Quantity[40600, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "This award provides funding to help cover the travel expenses of participants from the U.S. in the \"Workshop on partial differential equations and several complex variables\" that will be held August 3 - 7, 2015, in Serra Negra, Brazil.\n\nThe workshop will focus on recent developments in closely related areas of analysis and geometry, namely, several complex variables, overdetermined systems of partial differential equations, and CR geometry. Two mini-courses designed for graduate students and recent Ph.D.'s will form an important part of the workshop. The first mini-course will be taught by Mei-Chi Shaw who will lecture on Cauchy-Riemann equations in complex manifolds. The second mini-course will be on semi global solvability of complex vector fields and it will be taught by Abdelhamid Meziani. The workshop will provide opportunities for graduate students and recent Ph.D.'s to present and discuss their research results.", "AwardID" -> "1500692", "Institution" -> Entity["NSFInstitution", "TempleUniversity"], "Investigators" -> {Entity["NSFInvestigator", "ShiferawBerhanu"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500692&HistoricalAwards=false"], "KeywordTally" -> {{"complex", 4}, {"equations", 3}, {"recent", 3}, {"workshop", 3}, {"differential", 2}, {"geometry", 2}, {"graduate", 2}, {"mini-course", 2}, {"partial", 2}, {"Ph.D.'s", 2}, {"students", 2}, {"taught", 2}, {"variables", 2}}|>, "1500694" -> <|"AwardTitle" -> "Doctoral Dissertation Research: A Descriptive Grammar of Hakhun Tangsa", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2017, 4, 30}], "AwardAmount" -> Quantity[17377, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "A core communicative function of the clause includes identifying the participants in an activity. The amount and type of information that identifies \"who did what to whom\" can vary from language to language. In many languages a word or affix is used to indicate basic information on the person doing the action, i.e., 1st person (I, we) 2nd person, (you, you all), or 3rd person (he, she, they). In the northeast Indian language Hakhun Tangsa, if 3rd person acts on a 2nd person (he kissed you) or a 2nd acts on 1st (you kissed me), additional information, called inverse marking, must be added to the verb. \nInverse marking and other such distinctive features will be used by Krishna Boro to determine the place of Hakhun within the Tangsa family, which consists of over 30 languages, and the place of the Tangsa family within the Northern Naga branch of the Tibeto-Burman family. There are over 250 South Asian Tibeto-Burman languages but many of these are yet to be systematically documented and as a result the history of these languages remains unclear.\n\nUnder the direction of Scott DeLancey of the University of Oregon, Boro, who is himself a native speaker of a Tibeto-Burman language, will produce a comprehensive descriptive grammar of Hakhun Tangsa. The Hakhun grammar along with recordings and analysis will form a unique resource for the study of key grammatical features for reconstructing the language lineage of the Northern Naga languages. \n\nThe grammar will form the basis for a practical orthography and teaching materials for the Hakhun community. Krishana Boro will also train community members in language documentary methods so that they can continue language documentation in less accessible regions after the primary project is finished. \n\nAll materials created through this project will be archived at the Endangered Languages Archive.\n.", "AwardID" -> "1500694", "Institution" -> Entity["NSFInstitution", "UniversityOfOregonEugene"], "Investigators" -> {Entity["NSFInvestigator", "KrishnaBoro"], Entity["NSFInvestigator", "ScottDeLancey"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500694&HistoricalAwards=false"], "KeywordTally" -> {{"language", 7}, {"person", 6}, {"Hakhun", 5}, {"languages", 5}, {"Tangsa", 4}, {"2nd", 3}, {"Boro", 3}, {"family", 3}, {"grammar", 3}, {"information", 3}, {"Tibeto-Burman", 3}, {"1st", 2}, {"3rd", 2}, {"acts", 2}, {"br/>

", 2}, {"community", 2}, {"features", 2}, {"form", 2}, {"kissed", 2}, {"marking", 2}, {"materials", 2}, {"Naga", 2}, {"Northern", 2}, {"place", 2}, {"project", 2}, {"used", 2}}|>, "1500695" -> <|"AwardTitle" -> "RAPID: Documenting Endangered Languages Outreach Video Series", "AwardEffectiveDate" -> DateObject[{2015, 1, 1}], "AwardExpirationDate" -> DateObject[{2017, 3, 31}], "AwardAmount" -> Quantity[49469, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Recent advances in technology have created new methodologies in documenting endangered languages. This project will provide an overview of these advances in video format and will be presented by experts in field. The purpose of the project is to support production of the highest quality of documentary linguistic products and stimulate research in these areas. The primary audience for these outreach videos are linguists or language experts from minority communities who may engage in language documentation but do not have access to state-of-the-art instruction. Over the long term, greater participation in documenting endangered languages will contribute new knowledge of a wider array of under-documented endangered languages each of which provide unique information on human language and cognition.\n\nThe videos will be uploaded as YouTube videos and will be freely available online. They will include information on tools for language analysis (transcription, interlinear gloss creation, and acoustic analysis) and linguistic analysis needed for dictionary, grammar, and corpus creation. Experts will also review current standards in metadata creation and archiving, and funding mechanisms for documentary linguistic research.", "AwardID" -> "1500695", "Institution" -> Entity["NSFInstitution", "UniversityOfOklahomaNormanCampus"], "Investigators" -> {Entity["NSFInvestigator", "CarlosNash"], Entity["NSFInvestigator", "Racquel-MariaYamada"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "7914", "Text" -> "RAPID"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500695&HistoricalAwards=false"], "KeywordTally" -> {{"language", 4}, {"analysis", 3}, {"creation", 3}, {"endangered", 3}, {"languages", 3}, {"linguistic", 3}, {"videos", 3}, {"advances", 2}, {"documentary", 2}, {"documenting", 2}, {"experts", 2}, {"information", 2}, {"new", 2}, {"project", 2}, {"provide", 2}, {"research", 2}}|>, "1500696" -> <|"AwardTitle" -> "Long-Term Dynamics of Nonlinear Evolution Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[250000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Electricity, magnetism, light, and therefore information propagates by means of wave motion. While basic aspects of wave propagation were understood about three hundred years ago, technology and science demand methods to analyze more and more sophisticated phenomena relating to waves. For example, information for the internet is passed along glass fiber cables in the form of light as well as via satellites in space through electromagnetic waves. Cell phone technology operates essentially the same way. The dramatic increase in speed in internet communication today as compared to the mid 1990s, for example, is due to a complete and radical change in the design of glass fiber cables. Instead of using the same material for hundreds or thousands of miles, the current design alternates between different materials thus allowing for subtle nonlinear effects to come into play. This revolutionary design is the result of interactions between engineers, applied mathematicians, and material scientists. Advanced mathematics very closely related to the subject matter of this project played a decisive role in the process. Mathematicians working in partial differential equations are cognizant of the importance of training students in the sciences in order to meet the high demands of industry and government. \n\nThis project aims at understanding the long-term dynamics of solutions to various systems of nonlinear partial differential equation of wave type. This typically means hyperbolic equations, but it can also refer to the Schroedinger equation. While much progress has been made on the defocusing case, where waves exist for all times and scatter to the vacuum state, focusing equations are much less studied. This type of equation can exhibit finite time blowup as well as small data scattering. The main goal is to determine whether or not global solutions scatter to a stationary solution also known as a soliton. The latter seems likely if basic invariances of the equations, such those given by dilation and translation symmetries, are excluded. This is precisely the case for Klein-Gordon equations in the radial setting.", "AwardID" -> "1500696", "Institution" -> Entity["NSFInstitution", "UniversityOfChicago"], "Investigators" -> {Entity["NSFInvestigator", "WilhelmSchlag"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500696&HistoricalAwards=false"], "KeywordTally" -> {{"equations", 5}, {"design", 3}, {"equation", 3}, {"wave", 3}, {"waves", 3}, {"basic", 2}, {"cables", 2}, {"case", 2}, {"differential", 2}, {"example", 2}, {"fiber", 2}, {"glass", 2}, {"information", 2}, {"internet", 2}, {"light", 2}, {"material", 2}, {"means", 2}, {"nonlinear", 2}, {"partial", 2}, {"project", 2}, {"scatter", 2}, {"solutions", 2}, {"technology", 2}, {"type", 2}}|>, "1500699" -> <|"AwardTitle" -> "On structures of large graphs", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[129999, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "In recent years, large-scale networks become more and more important in many fields of science. Examples of such networks include not only traditional networks like transportation networks and computer networks, but also social networks (like Facebook) and biological neural networks (like human brains). Since graphs are mathematical models of these networks, the study of these large-scale networks demands a better understanding of the behavior of large graphs. The topics under study in this research project are concerned with fundamental properties of large graphs. Results on these questions will have strong impact on many areas of graph theory. In particular, structure results coming out of this project could lead to more efficient algorithms for related problems on large graphs. These algorithms would in turn impact the study of large-scale networks from the real world.\n\nTo be precise, the PI will study the following three fundamental problems: \n\n(1) He will characterize graphs that do not contain a large K_{3,n}-minor. (This graph is special because researchers in this area believe that it is the main reason for a high genus of a graph. The PI proposes to show that a 6-connected K_{3,n}-free graph must have a small genus or small tree-width.) \n\n(2) He will establish a splitter theorem for large 4-connectd graph. (These types of results are very fundamental and, as useful tools, they will have a very wide range of applications.) \n\n(3) He will characterize Petersen-free graphs that can be drawn on the projective plane. (There are reasons to believe that this class of graphs provide important building blocks for general Petersen-free graphs. A positive result here could shed new light on the general problem of characterizing Petersen-free graphs.)", "AwardID" -> "1500699", "Institution" -> Entity["NSFInstitution", "LouisianaStateUniversity&AgriculturalAndMechanicalCollege"], "Investigators" -> {Entity["NSFInvestigator", "GuoliDing"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500699&HistoricalAwards=false"], "KeywordTally" -> {{"networks", 10}, {"graphs", 9}, {"graph", 5}, {"large", 5}, {"study", 4}, {"fundamental", 3}, {"large-scale", 3}, {"like", 3}, {"Petersen-free", 3}, {"algorithms", 2}, {"believe", 2}, {"characterize", 2}, {"general", 2}, {"genus", 2}, {"impact", 2}, {"important", 2}, {"PI", 2}, {"problems", 2}, {"project", 2}, {"results", 2}, {"small", 2}}|>, "1500702" -> <|"AwardTitle" -> "Measure rigidity in Teichmuller space and beyond", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[125000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "This project deals with a long-standing problem related to randomness. Consider a ball on a frictionless table. If the ball is set in motion, it will travel forever, making perfectly elastic collisions with the walls. If the table is a square or an equilateral triangle, there are only two possible behaviors: either the ball repeats the same periodic path forever, or it travels completely randomly in the entire polygon, eventually visiting every part of the table. This project is directed toward the basic mathematical problem of understanding the behavior of a ball when the table is a more general polygon. This is a basic problem arising in physics and statistical mechanics.\n\nThe project concerns the interrelated analytic study of trajectories on rational polygonal tables, moduli spaces of abelian and quadratic differentials, and the dynamics of the action of the group of two-by-two matrices on these moduli spaces. In recent work with M. Mirzakhani and in part with A. Mohammadi the PI was able to prove some dynamical rigidity results for this action, which allow one to understand every (and not just almost every) orbit. This is important for several reasons. In particular, the surfaces which arise from table trajectories are a set of measure zero in the moduli space, and ergodic theorems which hold at every point are needed to prove results about the trajectories. Many of the results and techniques are based on a loose analogy with the theory of unipotent flows on locally symmetric spaces (e.g. Ratner's theorem). However, the moduli spaces of differentials are substantially different and new ideas were needed. We propose developing these ideas further, both in the context of dynamics on moduli space and also in the context of other group actions.", "AwardID" -> "1500702", "Institution" -> Entity["NSFInstitution", "UniversityOfChicago"], "Investigators" -> {Entity["NSFInvestigator", "AlexEskin"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500702&HistoricalAwards=false"], "KeywordTally" -> {{"moduli", 5}, {"table", 5}, {"ball", 4}, {"spaces", 4}, {"problem", 3}, {"project", 3}, {"results", 3}, {"trajectories", 3}, {"action", 2}, {"basic", 2}, {"context", 2}, {"differentials", 2}, {"dynamics", 2}, {"forever", 2}, {"group", 2}, {"ideas", 2}, {"needed", 2}, {"polygon", 2}, {"prove", 2}, {"set", 2}, {"space", 2}}|>, "1500703" -> <|"AwardTitle" -> "Inverse Problems and Spectral Theory for Elliptic Operators", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[129661, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The project is concerned with development of the mathematical theory for several fundamental inverse problems arising in science and technology, as well as with achieving advances in significant questions of spectral theory coming from problems of electromagnetism and quantum mechanics. Broadly speaking, in an inverse problem, one wishes to determine internal properties of a medium by performing measurements along the boundary of the medium. For instance, in electrical impedance tomography, one attempts to recover the conductivity of a body by making voltage and current measurements at the boundary. Since inverse problems are at the core of a variety of engineering and scientific investigations, including medical imaging, seismography, oil prospection, radar imaging, and non-destructive testing, any further progress in the mathematical theory of such problems will undoubtedly have real world applications. Spectral theory deals with the investigation of vibrations and their frequencies for a variety of different objects, ranging from atoms and molecules in chemistry to obstacles in acoustic waveguides. The fundamental issues, which are of great significance in many problems of science and engineering, from celestial to quantum mechanics, include deciding when such vibrations occur, how to go about computing their frequencies, as well as understanding the size and localization of the vibrations. The aim of the project is to advance our understanding of these issues by concentrating on model problems of quantum mechanics, specifically in the physically relevant regime of high frequencies.\n\n\nThe project addresses the following significant topics: the mathematical theory of inverse boundary problems for elliptic partial differential equations (PDE), harmonic analysis for elliptic PDE, and spectral theory of elliptic PDE with periodic coefficients. Although these topics have originated in distinct mathematical communities, recent work has shown that techniques and insights in the various topics are closely related and interact in a fruitful way. A novel idea of the project is to expand this interaction to solve significant problems in all of these areas. Despite an impressive body of results in the field of inverse problems obtained within the last 30 years, many fundamental questions still remain unsolved, including inverse problems for PDE with irregular coefficients, partial data problems when measurements are performed only on a portion of the boundary, and inverse problems on manifolds. The goal of the first part of the project is to attack these problems for several fundamental elliptic PDE, in particular the conductivity, magnetic Schroedinger, and polyharmonic equations, as well as the Maxwell system. The second topic is concerned with estimates for resolvents of elliptic operators on compact and non-compact manifolds, in Lebesgue spaces. Apart from their intrinsic significance in spectral and scattering theory, such estimates are crucial in control theory and inverse problems. The aim here is to understand how the dynamics of the underlying Hamilton flow of the operator and regularity of the coefficients each impacts on the spectral estimates. The third topic deals with the spectral theory of Schroedinger type operators with periodic coefficients, coming from solid state physics. A central question concerns the nature of the spectra of such operators, which one conjectures to be purely absolutely continuous. Long known in the Euclidean case, it is still wide open for general Laplace-Beltrami type operators. The objective is to resolve this conjecture in several significant special cases of Riemannian metrics.", "AwardID" -> "1500703", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Irvine"], "Investigators" -> {Entity["NSFInvestigator", "KatyaKrupchyk"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500703&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 14}, {"theory", 9}, {"inverse", 8}, {"elliptic", 5}, {"PDE", 5}, {"project", 5}, {"spectral", 5}, {"boundary", 4}, {"coefficients", 4}, {"fundamental", 4}, {"mathematical", 4}, {"operators", 4}, {"significant", 4}, {"estimates", 3}, {"measurements", 3}, {"mechanics", 3}, {"quantum", 3}, {"topics", 3}, {"vibrations", 3}, {"aim", 2}, {"body", 2}, {"coming", 2}, {"concerned", 2}, {"conductivity", 2}, {"deals", 2}, {"engineering", 2}, {"equations", 2}, {"frequencies", 2}, {"imaging", 2}, {"including", 2}, {"issues", 2}, {"manifolds", 2}, {"medium", 2}, {"partial", 2}, {"periodic", 2}, {"questions", 2}, {"Schroedinger", 2}, {"science", 2}, {"significance", 2}, {"topic", 2}, {"type", 2}, {"understanding", 2}, {"variety", 2}}|>, "1500704" -> <|"AwardTitle" -> "Problems in Operator Theory", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[99855, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Analysis of operators and inherent phenomena of noncommutativity have been developing in response to refinement of physical models of the world as well as to advancement of other sciences and technology. This project is devoted to open problems in operator theory that arise in mathematical physics, noncommutative analysis and geometry, and the theory of single-variable and multivariate operator functions. The project is also designed to strengthen connections between several areas of mathematics, contribute to general education, and enhance student research.\n\nThe proposed topics include establishing properties of operator functions with noncommuting arguments that are similar to classical properties of the respective scalar functions, understanding the impact of perturbations on spectral subspaces of operators, and studying the structure of elements belonging to operator algebras. The essence of the proposed research consists in developing innovative methods for handling different effects of noncommutativity that appear in the problems, and beyond. Such methods are expected to emerge from subtle synthesis of various techniques in analysis and operator theory.", "AwardID" -> "1500704", "Institution" -> Entity["NSFInstitution", "UniversityOfNewMexico"], "Investigators" -> {Entity["NSFInvestigator", "AnnaSkripka"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500704&HistoricalAwards=false"], "KeywordTally" -> {{"operator", 5}, {"functions", 3}, {"theory", 3}, {"analysis", 2}, {"developing", 2}, {"methods", 2}, {"noncommutativity", 2}, {"operators", 2}, {"problems", 2}, {"project", 2}, {"properties", 2}, {"proposed", 2}}|>, "1500707" -> <|"AwardTitle" -> "Harmonic Analysis Challenges in Nonlinear Dispersive Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[95488, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This research project explores the mathematical properties of a class of equations known as nonlinear dispersive equations. Equations of this type arise in models of several physical phenomena, including propagation of light in optical fibers, Bose-Einstein condensates, small-amplitude water waves, and waves in plasmas. Despite their common occurrence, understanding of the behavior of solutions to such equations is limited by their mathematical complexity. This project aims to extend current theoretical understanding of this important class of equations. Training of junior researchers and students in this area of research is also an integrated part of the project.\n\nThe problems to be investigated are nonlinear dispersive partial differential equations with broken symmetries and/or non-constant coefficients. While some of these equations are very physical, such as the cubic-quintic nonlinear Schrodinger equation with non-zero boundary conditions, others have been carefully selected by the investigator to highlight certain deficiencies in our mathematical understanding of the underlying linear propagator. A major thrust of this project is therefore to resolve questions in harmonic analysis related to the linear propagator in various geometries. These range from proving Strichartz estimates powerful enough to resolve the small data energy-critical problem on high-dimensional tori to shepherding recent progress on the restriction conjecture into the realm of non-constant coefficients, which is a key step toward resolving mass-critical problems outside the translation-invariant setting.", "AwardID" -> "1500707", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-LosAngeles"], "Investigators" -> {Entity["NSFInvestigator", "MonicaVisan"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500707&HistoricalAwards=false"], "KeywordTally" -> {{"equations", 6}, {"mathematical", 3}, {"nonlinear", 3}, {"project", 3}, {"understanding", 3}, {"class", 2}, {"coefficients", 2}, {"dispersive", 2}, {"linear", 2}, {"non-constant", 2}, {"physical", 2}, {"problems", 2}, {"propagator", 2}, {"research", 2}, {"resolve", 2}, {"waves", 2}}|>, "1500710" -> <|"AwardTitle" -> "The 29th Automorphic Forms Workshop", "AwardEffectiveDate" -> DateObject[{2015, 2, 15}], "AwardExpirationDate" -> DateObject[{2017, 1, 31}], "AwardAmount" -> Quantity[19220, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Matthew Douglass", "Abstract" -> "The 29th Annual Automorphic Forms Workshop (AFW) will be held March 2-5, 2015 at the University of Michigan in Ann Arbor, Michigan. Over the past three decades, the AFW has built a reputation as an internationally-recognized, well-respected conference attended by leading experts and junior researchers alike. The workshop is known for its inclusive, supportive atmosphere. Historically, about half of the presentations are given by mathematicians at early stages of their careers. Additionally, the workshop has a long history of involving women and members of other underrepresented groups in the automorphic forms community and facilitating the establishment of research connections. The workshop has led to many collaborations and research papers. Moreover, the workshop traditionally includes panel discussions on topics designed to further the mathematical careers of junior participants. This award supports participation in the workshop of twenty early-career U.S.-based mathematicians, including students. Additional information can be found at the workshop's website: automorphicformsworkshop.org.\n\nAutomorphic forms, in all of their various guises, are of central importance in modern number theory and illuminate deep connections between number theory and other mathematical disciplines including coding theory, mathematical physics, representation theory and topology. Some of the most remarkable mathematical breakthroughs of the 20th century, for instance Wiles' proof of Fermat's Last Theorem, made extensive use of automorphic forms. Moreover, several celebrated conjectures, such as those of Langlands and Bloch-Kato, are automorphic in nature. Many important classes of automorphic forms have only recently been discovered, for instance the harmonic Maass forms and mock modular forms that underlie Ramanujan's mock theta functions. The 29th AFW will feature talks on all aspects of automorphic forms with a special emphasis on mock modular forms and their applications. The workshop will highlight recent developments in the field and catalyze future research progress.", "AwardID" -> "1500710", "Institution" -> Entity["NSFInstitution", "UniversityOfMichiganAnnArbor"], "Investigators" -> {Entity["NSFInvestigator", "BenjaminLinowitz"], Entity["NSFInvestigator", "MaheshAgarwal"], Entity["NSFInvestigator", "LolaThompson"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500710&HistoricalAwards=false"], "KeywordTally" -> {{"forms", 8}, {"workshop", 6}, {"automorphic", 5}, {"mathematical", 4}, {"theory", 4}, {"AFW", 3}, {"mock", 3}, {"research", 3}, {"29th", 2}, {"careers", 2}, {"connections", 2}, {"including", 2}, {"instance", 2}, {"junior", 2}, {"mathematicians", 2}, {"Michigan", 2}, {"modular", 2}, {"Moreover", 2}, {"number", 2}}|>, "1500713" -> <|"AwardTitle" -> "EAGER-DynamicData: Judicious Censoring, Random Sketching, and Efficient Validate for Learning Patterns from Dynamically-Changing and Large-Scale Data Sets", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2017, 8, 31}], "AwardAmount" -> Quantity[300000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07010000", "ProgramOfficer" -> "Chengshan Xiao", "Abstract" -> "Abstract. With pervasive sensors continuously collecting and recording massive amounts of information, there is no doubt this is an era of data deluge. Learning from these dynamic and large volumes of data is expected to bring significant science and engineering advances along with consequent improvements in quality of life. The present early-concept grant for exploratory research aims to develop potentially transformative pattern recognition techniques that will be specifically tested on dynamically deforming (due to e.g., patient motion) cardiac magnetic resonance images, as well as on information extraction from large-scale healthcare datasets. Big challenges that this project addresses, include the sheer volume of online and growing datasets, which makes it impossible to run analytics especially in batch form; and also the facts that large-scale datasets are inevitably noisy, dynamic, incomplete, prone to outliers and (un)intentional misses, as well as vulnerable to cyber-attacks. The project's large-scale analytics will also permeate interdisciplinary benefits to environmental data mining, neuroscience, and the future power grid. At a broader scale, the developed technologies will provide valuable tools for foundational science and engineering research, and promote societal embracing of the emergent big data technologies, along with training the next-generation of data science professionals.\n\nThis early-concept grant for exploratory research aspires to tackle big data challenges by putting forth large-scale learning tools and their performance analyses that leverage two untested, but potentially transformative, ideas for extracting computationally affordable yet informative subsets of massive and dynamic datasets, namely i) adaptive censoring, and ii) random data sketching-and-validation. Data in this project can be stationary or nonstationary; they become available in batch or sequential (a.k.a. online) modes; they can be collected in vectors, matrices or general multi-way arrays (called tensors); noise, possibly outliers and (un)intentional misses are present; and data processing can be linear or nonlinear in adaptive or non-adaptive modes. The proposed high risk-high payoff research lies at the intersection of essential big data tools including compressive sampling, matrix and tensor completion, anomaly and outlier identification, online and parallel optimization techniques. In accordance with the major inference tasks, three intertwined research thrusts will be pursued: T1) Adaptive censoring for large-scale regressions; T2) Subspace tracking and imputation for dynamic large-scale tensors; and T3) Sketch-and-validate for large-scale clustering and classification. The resultant innovative tools will be tested in healthcare data, and multi-dimensional magnetic resonance imaging, having as ultimate goal high-resolution biomedical movies to be acquired, processed, and displayed in real time.", "AwardID" -> "1500713", "Institution" -> Entity["NSFInstitution", "UniversityOfMinnesota-TwinCities"], "Investigators" -> {Entity["NSFInvestigator", "GeorgiosGiannakis"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Electrical, Commun & Cyber Sys", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500713&HistoricalAwards=false"], "KeywordTally" -> {{"data", 10}, {"large-scale", 7}, {"research", 5}, {"datasets", 4}, {"dynamic", 4}, {"tools", 4}, {"big", 3}, {"online", 3}, {"science", 3}, {"adaptive", 2}, {"analytics", 2}, {"batch", 2}, {"censoring", 2}, {"challenges", 2}, {"early-concept", 2}, {"engineering", 2}, {"exploratory", 2}, {"grant", 2}, {"healthcare", 2}, {"information", 2}, {"magnetic", 2}, {"massive", 2}, {"misses", 2}, {"modes", 2}, {"outliers", 2}, {"potentially", 2}, {"present", 2}, {"project", 2}, {"resonance", 2}, {"techniques", 2}, {"technologies", 2}, {"tensors", 2}, {"tested", 2}, {"transformative", 2}, {"un)intentional", 2}}|>, "1500714" -> <|"AwardTitle" -> "Documenting Linguistic Structure and Language Change in Yawarana", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[299998, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "It is known that language change is inevitable and systematic and that genetically related languages often exhibit parallel changes. The Cariban languages, which constitute one of the largest linguistic families of South America, are a good testing ground for this expectation since closely related Cariban languages often show dissimilar changes.\n\nSpike Gildea of the University of Oregon along with linguist Natalia Cáceres and lexicographer Marie-Claude Mattei Muller will document a critically endangered Cariban language Yawarana [yar]. Extant data for Yawarana show surprising phonological differences (e.g., syllable reduction, stress) with closely related languages, Mapoyo and 'Pémono. In addition, there are dramatic differences in morphosyntax (e.g., case alignment, verbal conjugations) between Yawarana, Mapoyo, and 'Pémono and their Cariban neighbors Panare, 'Tamanaku, and Ye'kwana. Particularly striking are differences between main clause verb forms resulting from nominalizations (like English 'eating' or 'eater' based on 'eat') or a participial (like English 'eaten' based on 'eat'). All languages change, and some entirely replace verb conjugations with nominalizations and participles, but it is unusual for a language or language group to have made so complete a change when the nearest related languages have not.\n\nTo investigate these and additional grammatical features of Yawarana, this team will work with the last speakers of the language to produce a state-of-the-art documentary corpus, including audio and video recordings of Yawarana speech with annotations and analysis of speech samples. The final products will include a reference grammar and a Yawarana-Spanish bilingual dictionary. The resulting data will elucidate the nature of language change in Cariban and will have implications for theories of language change.\n\nGildea and his team will collaborate with the Venezuelan Ministry of Education in their efforts to produce educational materials about the Yawarana language for use in speech community schools. The documentary corpus created for this project will be archived at the Archive of the Indigenous Languages of Latin America (University of Texas).\n\nThe project is supported by co-funds from the National Science Foundation's International Science and Engineering Office.", "AwardID" -> "1500714", "Institution" -> Entity["NSFInstitution", "UniversityOfOregonEugene"], "Investigators" -> {Entity["NSFInvestigator", "SpikeGildea"], Entity["NSFInvestigator", "NataliaCaceres"]}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500714&HistoricalAwards=false"], "KeywordTally" -> {{"language", 8}, {"languages", 6}, {"Yawarana", 6}, {"Cariban", 5}, {"change", 4}, {"related", 4}, {"differences", 3}, {"speech", 3}, {"America", 2}, {"based", 2}, {"closely", 2}, {"conjugations", 2}, {"corpus", 2}, {"data", 2}, {"documentary", 2}, {"eat", 2}, {"e.g", 2}, {"English", 2}, {"like", 2}, {"Mapoyo", 2}, {"nominalizations", 2}, {"Pémono", 2}, {"produce", 2}, {"project", 2}, {"resulting", 2}, {"Science", 2}, {"team", 2}, {"University", 2}, {"verb", 2}}|>, "1500720" -> <|"AwardTitle" -> "Documentation and Child Learners: A Workshop to Examine the Broader Impacts of Endangered Language Documentation", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2017, 4, 30}], "AwardAmount" -> Quantity[50000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Current research indicates that 46% of the world's 7,000 languages are in danger of losing their last speakers by the end of this century. Communities are responding to this situation by accelerating their efforts to learn their languages. In situations of severe language endangerment, communities and educators are turning to archived language documentation to promote language learning. This workshop project will investigate the process of language acquisition in these unique learning situations, looking specifically at the role of documentary materials -- grammars, dictionary, and linguistically analyzed natural discourse -- in learning. A special focus will be on the long-term academic success and other benefits to learners.\n\nIn Fall 2015, Ruth Rouvier of the Education Development Center will facilitate this workshop in Washington D.C. Rouvier will bring together a 10-member interdisciplinary team of specialists in language acquisition, early childhood development, educational linguistics, documentary linguistics, statistics, and public health. Participants will address topics relating to the role of language documentation in formal language-based activities and the impact of these activities on learners ages 0-5. The impacts to be addressed include linguistic benefits (language competence and use) and extra-linguistic benefits relating to academic success and social well-being. Workshop participants will examine both the resources and practices known or hypothesized to result in these positive outcomes, and the methods for evaluating these benefits. They will assess the state of collective (i.e., academic, professional and community) knowledge regarding these issues and make recommendations for addressing shortfalls, in order to encourage research on how language documentation research affects society.\n\nResults of the workshop will be broadly disseminated for discussion and comment through listservs such as the Resource Network for Linguistic Diversity, the Foundation for Endangered Languages), and the Linguistlist.", "AwardID" -> "1500720", "Institution" -> Entity["NSFInstitution", "EducationDevelopmentCenter"], "Investigators" -> {Entity["NSFInvestigator", "RuthRouvier"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500720&HistoricalAwards=false"], "KeywordTally" -> {{"language", 8}, {"benefits", 4}, {"academic", 3}, {"documentation", 3}, {"learning", 3}, {"research", 3}, {"workshop", 3}, {"acquisition", 2}, {"activities", 2}, {"documentary", 2}, {"languages", 2}, {"linguistics", 2}, {"relating", 2}, {"role", 2}, {"Rouvier", 2}, {"situations", 2}, {"success", 2}}|>, "1500724" -> <|"AwardTitle" -> "Committee on Geological and Geotechnical Engineering and its Activities", "AwardEffectiveDate" -> DateObject[{2015, 5, 15}], "AwardExpirationDate" -> DateObject[{2020, 4, 30}], "AwardAmount" -> Quantity[385000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "07030000", "ProgramOfficer" -> "Richard J. Fragaszy", "Abstract" -> "This award provides core funding for the Committee on Geological and Geotechnical Engineering (COGGE), a standing committee under the National Research Council's Board on Earth Sciences and Resources. COGGE is the focal point within the Board on Earth Sciences and Resources for scientific, technical, and public-policy issues pertaining to the engineering applications of Earth Sciences. The committee's scope encompasses Earth processes and materials, including the mechanics of rock and soil, and focuses on safe and responsible human development, risk assessment, and mitigation of natural anthropogenic hazards. The committee organizes and oversees studies: 1) to identify, investigate, and report on questions relating to geological and geotechnical engineering to government, industry, academia, and the public; 2) to provide scientific and technical information to inform public policy on geological and geotechnical engineering issues; 3) to identify new technologies and potential applications; and, 4) to promote the acquisition and dissemination of knowledge. In addition, the committee provides a forum for discussion among academic and professional groups, government agencies, and private industry to enhance national and international cooperation and exchange of information. \n\nThe committee activity spans all areas of geological and geotechnical engineering, will identify new areas of needed research, and will provide increased understanding of the importance of geotechnology in addressing societal needs. The COGGE's mission is driven by the need to promote the responsibility of the geoengineer throughout the lifecycle of geoengineered facilities and structures; from site selection and facility design, to construction, operation, maintenance, and decommissioning. Issues include the geoengineering concerns associated with natural and built environments, radioactive and hazardous waste isolation and remediation, mitigation of natural hazards (e.g. earthquakes, landslides, rising sea levels), environmentally sound and safe recovery of natural resources, and interest in defense structures in rock. Projects undertaken, whether mandated by Congress, requested by federal agencies, or self-initiated, will be conducted by ad hoc committees under COGGE. Projects, governed by NRC guidelines, will result in peer-reviewed reports, and will provide geoengineering advice for decision makers.", "AwardID" -> "1500724", "Institution" -> Entity["NSFInstitution", "NationalAcademyOfSciences"], "Investigators" -> {Entity["NSFInvestigator", "SammanthaMagsino"]}, "ProgramElements" -> {{"Code" -> "1636", "Text" -> "Geotechnical Engineering and M"}}, "ProgramReferences" -> {{"Code" -> "036E", "Text" -> "CIVIL INFRASTRUCTURE"}, {"Code" -> "037E", "Text" -> "GEOTECHNICAL ENGINEERING"}, {"Code" -> "1057", "Text" -> "CIS BASE RESEARCH"}, {"Code" -> "1576", "Text" -> "NATIONL EARTHQK HZRD REDCT PRG"}, {"Code" -> "172E", "Text" -> "Geomechanics"}, {"Code" -> "9102", "Text" -> "WOMEN, MINORITY, DISABLED, NEC"}, {"Code" -> "CVIS", "Text" -> "CIVIL INFRASTRUCTURE"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Civil, Mechanical, & Manufact Inn", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500724&HistoricalAwards=false"], "KeywordTally" -> {{"committee", 4}, {"Earth", 4}, {"engineering", 4}, {"natural", 4}, {"COGGE", 3}, {"geological", 3}, {"geotechnical", 3}, {"identify", 3}, {"provide", 3}, {"Sciences", 3}, {"agencies", 2}, {"applications", 2}, {"areas", 2}, {"Board", 2}, {"geoengineering", 2}, {"government", 2}, {"hazards", 2}, {"industry", 2}, {"information", 2}, {"issues", 2}, {"mitigation", 2}, {"new", 2}, {"Projects", 2}, {"promote", 2}, {"provides", 2}, {"public", 2}, {"Resources", 2}, {"rock", 2}, {"safe", 2}, {"scientific", 2}, {"structures", 2}, {"technical", 2}}|>, "1500730" -> <|"AwardTitle" -> "Doctoral Dissertation Research: Acquisition of Complex Chickasaw Linguistic Constructions in an Endangered Language Context", "AwardEffectiveDate" -> DateObject[{2015, 7, 15}], "AwardExpirationDate" -> DateObject[{2017, 6, 30}], "AwardAmount" -> Quantity[17216, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Learners of major world languages can acquire fluency in an additional language through formal instruction or informally through immersion in a speech community. Formal and informal learning reflect different levels and types of analytic and adaptive processes. Juliet Morgan under the direction of Racquel Yamada of the University of Oklahoma will investigate the learning processes involved in acquiring fluency in Chickasaw [cic], a Muskogean language spoken in Oklahoma by approximately 65 fluent first language speakers, all over the age of fifty. The project will explore learning processes in this unique case where formal instruction and informal exposure are highly constrained due to the low functional use of the language.\n\nJuliet Morgan will collect data from adult learners of Chickasaw involved in the Master-Apprentice language learning program. Developed specifically for teaching endangered languages, the Master-Apprentice teaching method pairs a fluent elder with a learner or group of learners who meet multiple times a week for the purpose of communicating exclusively in the endangered language. Using ethnographic and language documentation methodologies, Morgan will collect cross-sectional and longitudinal data from Chickasaw apprentices. Analyzing the input and output of these interactions, she will analyze the order of acquisition, developmental stages, and learner varieties. Morgan will focus on how the learners' use of morphosyntax (how they create words and sentences) and discourse (how they organize sentence into larger linguistic units) approximates the elder's variety. Additionally, the research will investigate how the elder fluent speakers perceive the speech of the L2 learner. \n\nAcquisition studies of indigenous languages are rare since fluent speakers and language teaching materials are often unavailable for language teaching and learning to occur. Opportunities to conduct studies of this sort are quickly declining, as the number of fluent native speakers dwindles faster than the number of emerging fluent learners. Juliet Morgan's research provides unparalleled access to information on learning with these unique set of variables. \n\nThis research will have implications for the Chickasaw Nation language revitalization efforts by providing the means to assess what is most effective in the Master-Apprentice method.", "AwardID" -> "1500730", "Institution" -> Entity["NSFInstitution", "UniversityOfOklahomaNormanCampus"], "Investigators" -> {Entity["NSFInvestigator", "Racquel-MariaYamada"], Entity["NSFInvestigator", "JulietMorgan"]}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500730&HistoricalAwards=false"], "KeywordTally" -> {{"language", 9}, {"fluent", 6}, {"learning", 6}, {"Chickasaw", 4}, {"learners", 4}, {"Morgan", 4}, {"speakers", 4}, {"teaching", 4}, {"languages", 3}, {"learner", 3}, {"Master-Apprentice", 3}, {"processes", 3}, {"research", 3}, {"collect", 2}, {"data", 2}, {"elder", 2}, {"endangered", 2}, {"fluency", 2}, {"formal", 2}, {"informal", 2}, {"instruction", 2}, {"investigate", 2}, {"involved", 2}, {"Juliet", 2}, {"method", 2}, {"number", 2}, {"Oklahoma", 2}, {"speech", 2}, {"studies", 2}, {"unique", 2}, {"use", 2}}|>, "1500738" -> <|"AwardTitle" -> "Collaborative Research: Contributions of Endangered Language Data for Advances in Technology-enhanced Speech Annotation", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[237505, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Linguists have increased efforts to collect authentic speech materials from endangered and little-studied languages to discover linguistic diversity. However, the challenge of transcribing these speech into written form to facilitate analysis is daunting. This is because of both the sheer quantity of digitally collected speech that needs to be transcribed and the difficulty of unpacking the sounds of spoken speech. \n\nLinguist Andreas Kathol and computer scientist Vikramjit Mitra of SRI international and linguist Jonathan D. Amith of Gettysburg College will team up to create software that can substantially reduce the language transcription bottleneck. Using as a test case Yoloxochitl Mixtec, an endangered language from the state of Guerrero, Mexico, the team will develop a software tool that will use previously transcribed Yoloxochitl Mixtec speech data to both train a new generation of native speakers in practical orthography and to develop automatic speech recognition software. The output of the recognition software will be used as preliminary transcription that native speakers will correct, as necessary, to create additional high-quality training data. This recursive method will create corpus of transcribed speech large enough so that software will be able to complete automatic transcription of newly collected speech materials.\n\nThe project will include the training of undergraduate and graduate students in software development and the analysis of the Yoloxochitl Mixtec sound system. The project will also train native speakers as documenters in an interactive fashion that systematically introduces them to the transcription conventions of their language. This software tool will help in establishing literacy in Yoloxochitl Mixtec among a broader base of speakers.\n\nThe results of this project will be available at the Archive of Indigenous Languages of Latin America (University of Texas, Austin), Kaipuleohone (University of Hawai'i Digital Language Archive), and at the Linguistic Data Consortium (University of Pennsylvania).", "AwardID" -> "1500738", "Institution" -> Entity["NSFInstitution", "SRIInternational"], "Investigators" -> {Entity["NSFInvestigator", "VikramjitMitra"], Entity["NSFInvestigator", "AndreasKathol"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "7719", "Text" -> "DEL"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}, {"Code" -> "7298", "Text" -> "COLLABORATIVE RESEARCH"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500738&HistoricalAwards=false"], "KeywordTally" -> {{"speech", 8}, {"software", 7}, {"Mixtec", 4}, {"transcription", 4}, {"Yoloxochitl", 4}, {"create", 3}, {"language", 3}, {"native", 3}, {"project", 3}, {"speakers", 3}, {"transcribed", 3}, {"University", 3}, {"analysis", 2}, {"Archive", 2}, {"automatic", 2}, {"collected", 2}, {"data", 2}, {"develop", 2}, {"endangered", 2}, {"recognition", 2}, {"team", 2}, {"tool", 2}, {"train", 2}, {"training", 2}}|>, "1500743" -> <|"AwardTitle" -> "Arithmetic on Shimura Varieties and Applications", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[239998, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "Mathematics has always been essential to the development of science and technology. Now mathematics is becoming increasingly important, too, to business, finance, biology, and social sciences. Basic research in mathematics, which is thought of as \"pure\" mathematics, is increasingly finding deep applications in unexpected areas. The research area of this project has this flavor. On the one hand, the principal investigator is investigating Shimura varieties, whose definition itself involves both geometry and representation theory. These objects lie at the center of modern number theory. In their simplest cases, the modular curves, they have been studied for more than one hundred years and were essential to the proof of Fermat's Last Theorem, one of the most famous and oldest conjectures in mathematics. On the other hand, the investigator's research results in recent years have become useful in algebraic curve cryptosystems. These are essential to the safety of electronic commerce and communication. The investigator will continue to work on these types of applications. \n\nIn one of the projects joint with Bruinier, Howard, Kudla, and Rapoport, the investigator aims to prove that a generating function of arithmetic Chow cycles in the Shimura varieties of unitary type is modular. As an application, he will prove more non-Abelian cases of the Colmez Conjecture. In another project, the investigator will try to understand the L-function side of the Colmez conjecture and obtain clues on how to attack the general case. In yet another project, the investigator will study, with collaborators, CM values of some interesting Borcherds projects. These have two purposes: one is to prove some classical conjectures, and the other is an application to cryptosystems.", "AwardID" -> "1500743", "Institution" -> Entity["NSFInstitution", "UniversityOfWisconsin-Madison"], "Investigators" -> {Entity["NSFInvestigator", "TonghaiYang"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500743&HistoricalAwards=false"], "KeywordTally" -> {{"investigator", 5}, {"mathematics", 4}, {"essential", 3}, {"project", 3}, {"prove", 3}, {"research", 3}, {"application", 2}, {"applications", 2}, {"cases", 2}, {"Colmez", 2}, {"conjectures", 2}, {"cryptosystems", 2}, {"hand", 2}, {"increasingly", 2}, {"modular", 2}, {"projects", 2}, {"Shimura", 2}, {"theory", 2}, {"varieties", 2}, {"years", 2}}|>, "1500750" -> <|"AwardTitle" -> "Dynamical Developments: A Conference in Complex Dynamics and Teichmuller Theory", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 5, 31}], "AwardAmount" -> Quantity[49950, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "This award supports the participation of U.S.-based researchers in the international conference \"Dynamical Developments: A Conference in Complex Dynamics and Teichmüller theory,\" taking place August 17-21, 2015, at Jacobs University in Bremen, Germany. Dynamical systems are all around us: the motion of the planets, the weather, the stock market, and the ecosystems in which we live. These systems depend on a variety of parameters, and as these parameters change, the corresponding system is affected. Often, \"complexifying\" a dynamical system and its corresponding parameter space, that is, regarding the salient quantities as complex numbers rather than (the more highly restricted) real numbers, leads to new insights and tools for investigating the underlying mathematics. Complex dynamics is a very active field that has experienced tremendous progress over the past few decades. This conference will bring together a diverse group of participants, ranging from various experts in these fields to younger researchers who are beginning their studies, for an intense and focused meeting to discuss exciting new developments, ideas, and directions for the subject.\n\nComplex dynamics has thrived over the past 25 years. This period of development has led to deep results on certain one-parameter model families (quadratic polynomials, for example). The time is ripe for the subject to advance to a more general theory, which will inevitably involve related fields such as Teichmüller theory, moduli spaces, dynamics in several complex variables, self-similar groups, arithmetic dynamics, symbolic dynamics, hyperbolic and algebraic geometry, and statistical physics. The conference will feature presentations by leading experts in complex dynamics and Teichmüller theory and will provide ample time for discussions. In addition to the formal scientific program, this conference will have two aspects less common to current mathematics conferences: there will be a young researchers seminar in which more junior participants can share their work with the community of mathematicians attending the conference, and there will be a computer program tutorial, showcasing some of the latest software used in the field. \n\nConference web site : http://www-personal.umich.edu/~kochsc/H70.html", "AwardID" -> "1500750", "Institution" -> Entity["NSFInstitution", "UniversityOfMichiganAnnArbor"], "Investigators" -> {Entity["NSFInvestigator", "SarahKoch"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500750&HistoricalAwards=false"], "KeywordTally" -> {{"dynamics", 6}, {"conference", 5}, {"theory", 4}, {"complex", 3}, {"researchers", 3}, {"Teichmüller", 3}, {"Complex", 2}, {"corresponding", 2}, {"Dynamical", 2}, {"experts", 2}, {"field", 2}, {"fields", 2}, {"mathematics", 2}, {"new", 2}, {"numbers", 2}, {"parameters", 2}, {"participants", 2}, {"past", 2}, {"program", 2}, {"system", 2}, {"systems", 2}, {"time", 2}}|>, "1500751" -> <|"AwardTitle" -> "Typological and historical discovery through language documentation of Walman, Srenge, Aro, and Eho, four critically endangered languages", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[299570, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "About one fifth of the languages of the world (that is, over 1200 languages) are spoken in New Guinea. This is more than all the languages of mainland Europe and Asia combined. Yet fewer than 5% of the languages of New Guinea have been described in any detail and for the majority, we know next to nothing. We know from past experience that New Guinean languages exhibit rare typological features through which we can understand better how language changes through time and how language systems are organized. We must document these features now as many of the languages of New Guinea are seriously endangered and are no longer being learned by young children. Probably a majority of the languages of New Guinea will be extinct or almost extinct by the end of this century. Language is the most complex form of human behavior, but for every language that become extinct, we forever lose knowledge about this essential part of what it means to be human. \n\nMatthew Dryer of SUNY at Buffalo along with linguist Pamela Brown and two graduate students will conduct fieldwork in northern New Guinea in or near the Torricelli Mountains. They will complete or create dictionaries, grammars and texts collections for four languages, Walman, Srenge, Aro, and Eho, all of which are of the Torricelli group. The documentation will include descriptions of complex verbal conjunction, typologically unusual infixation patterns, and variations in word order that are determined by the object's thematic role. \n\nThe data collected from this project will be accessible from the Endangered Languages Archive.", "AwardID" -> "1500751", "Institution" -> Entity["NSFInstitution", "SUNYAtBuffalo"], "Investigators" -> {Entity["NSFInvestigator", "MatthewDryer"], Entity["NSFInvestigator", "PamelaBrown"]}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500751&HistoricalAwards=false"], "KeywordTally" -> {{"languages", 8}, {"New", 6}, {"Guinea", 5}, {"extinct", 3}, {"language", 3}, {"complex", 2}, {"features", 2}, {"human", 2}, {"know", 2}, {"majority", 2}, {"Torricelli", 2}}|>, "1500753" -> <|"AwardTitle" -> "Software for enriching endangered language-annotated databases with crowd-sourced linguistic and cultural input", "AwardEffectiveDate" -> DateObject[{2015, 4, 15}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[325793, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "To understand how humans organize and relay information, linguists need to know what linguistic structures are possible in human language. Yet many languages that can tell us more about potential linguistic structures are no longer being spoken as fluent older speakers are not being replaced by younger speakers, thus making the loss of linguistic and cultural knowledge irreversible. The Documenting Endangered Languages Program supports proposals, including those that create innovative software, to facilitate the efficient, rapid, and accurate digital capture of endangered language data so that this knowledge can be collected, analyzed, and made available for speakers and scientists in perpetuity.\n\nWith a three-year award Raphael Finkel of the University of Kentucky and Daniel Kaufmann of the Endangered Language Alliance will create software that allows for the rapid refinement of transcription and translation of endangered language data. The team will test their software on data collected on two languages -- Purhepecha, an isolate spoken in Mexico, and Koda, a Munda language spoken in Bangladesh and India. \n\nA central product of language documentation projects is the annotated corpus, a collection of language samples with accompanying analytic notes on specific features such as the sounds and word and sentence structure of the language. Kaufman and Finkel will write software that will provide web-based access to the corpus and make it possible for linguists and the speaker-community to search, browse, and edit the corpus. These additional participatory annotations will enrich and refine the corpus in ways and at a rate not previously possible. Thus, in addition to providing valuable data on two under-described languages, the results of this project have the potential of dramatically changing the quality of language documentation products. Data from these projects will be available at the Archive of the Indigenous languages of Latin America and the Endangered Languages Archive and Repository. The resulting software will be distributed through SourceForge.", "AwardID" -> "1500753", "Institution" -> Entity["NSFInstitution", "UniversityOfKentuckyResearchFoundation"], "Investigators" -> {Entity["NSFInvestigator", "RaphaelFinkel"], Entity["NSFInvestigator", "DanielKaufman"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500753&HistoricalAwards=false"], "KeywordTally" -> {{"language", 8}, {"software", 5}, {"corpus", 4}, {"data", 4}, {"languages", 4}, {"Endangered", 3}, {"linguistic", 3}, {"possible", 3}, {"speakers", 3}, {"spoken", 3}, {"Archive", 2}, {"available", 2}, {"collected", 2}, {"create", 2}, {"documentation", 2}, {"endangered", 2}, {"Finkel", 2}, {"knowledge", 2}, {"Languages", 2}, {"linguists", 2}, {"potential", 2}, {"projects", 2}, {"rapid", 2}, {"structures", 2}}|>, "1500755" -> <|"AwardTitle" -> "Analyzing Siriano and Desano to Determine Universal Principles of Language Change", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 12, 31}], "AwardAmount" -> Quantity[180883, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "A finely balanced linguistic ecology is needed to sustain the practice of linguistic exogamy which ensures that marriage occurs between speakers of different languages. These linguistic ecologies and the languages used to sustain them can begin to breakdown as speakers transition to larger world languages. Siriano and Desano, two languages of Northeastern Amazonia, have traditionally been maintained through linguistic exogamic practices which are now breaking down with the increasing influence of Brazilian Portuguese and Spanish. \n\nWilson Silva of the Rochester Institute of Technology will undertake a three-year study of Siriano [sir] and Desano [des] before further influence of language contact makes this difficult. These languages exhibit a number of typologically noteworthy features of broad scholarly interest such nasal harmony (where nasality extends over several segments), tone (the use of pitch for meaningful contrasts), noun classifiers (classifying nouns grammatically in terms of universal semantic parameters), and evidentiality (indicating what kinds of evidence are available for a given statement). Research products will include a linguistically annotated database, a reference grammar for Desano, audio and video documentation and preliminary description of Siriano. Silva's research will be useful in reconstructing the genetic relationship among languages of the Vaupés Linguistic Area to which Desano and Siriano belong. Understanding the structures of these closely related languages of the Eastern Tukanoan branch of the Tukanoan family will shed light on the nature of language change through contact with other languages.\n\nThis project has strong support from the communities and their leaders, and involves close collaboration between researchers and community members in Colombia and Brazil where these languages are spoken. The corpus of audiovisual and audio recordings collected as a result of this research will be archived at the Archive of the Indigenous Language of Latin America at the University of Texas at Austin and at the Museum of the Indian at National Foundation of the Indian (Museu do Índio at the Fundação Nacional do Índio), Brazil.", "AwardID" -> "1500755", "Institution" -> Entity["NSFInstitution", "RochesterInstituteOfTech"], "Investigators" -> {Entity["NSFInvestigator", "WilsonSilva"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> "5913", "Text" -> "BRAZIL"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "9178", "Text" -> "UNDERGRADUATE EDUCATION"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500755&HistoricalAwards=false"], "KeywordTally" -> {{"languages", 8}, {"Desano", 4}, {"linguistic", 4}, {"Siriano", 4}, {"audio", 2}, {"Brazil", 2}, {"contact", 2}, {"Indian", 2}, {"Índio", 2}, {"influence", 2}, {"language", 2}, {"research", 2}, {"speakers", 2}, {"sustain", 2}, {"Tukanoan", 2}}|>, "1500759" -> <|"AwardTitle" -> "Langlands Reciprocity and Automorphic Forms", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[270000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "This research project concerns reciprocity laws, which are correspondences between different sets of objects preserving certain quantities, each defined by separate means. Reciprocity laws are found in abundance in many disciplines, ranging from mathematics and physics to engineering, network theory, and social sciences. The two sets of objects may a priori have no way of seeing each other and that makes such laws truly fascinating. One of the deepest examples of reciprocity are those appearing in number theory, a rather general form of which is due to Artin and Langlands, for which the famous \"Quadratic Reciprocity Law\" is just a first example. \n\nSuch reciprocity laws suggest an indexing of certain presentations of \"Galois groups\" by complex matrices, objects of arithmetic nature, with infinite dimensional presentations of general linear groups over local fields, objects of analytic nature, preserving certain complex functions (root numbers and L-functions) attached to them by totally separate means. An important part of this project is to show that this reciprocity is robust by developing an approach to establishing this equality for all such factors. More precisely, this project suggests an approach to establishing the equality of certain Artin factors (Artin root numbers and L-functions) with those obtained from analytic methods, e.g., those coming from Langlands-Shahidi method. These will carry information from one side to the other including equality of conductors, root numbers and possibly R-groups. There will be consequences in representation theory and automorphic forms such as many cases of tempered L-packet and its converse, generic A-packet conjectures, as well as normalization of intertwining operators by means of Artin factors as demanded by Arthur and Langlands and the conjecture of Lapid and Mao as well as others. As another project, one hopes to obtain results on p-adic L-functions by means of Fourier coefficients of Eisenstein series where their complex versions show up. Certain intertwining relations for covering groups will also be established, as well as study of Weyl's law by means of twisted trace formula as part of a student doctorate thesis. The project suggests training of graduate students through teaching courses, mentoring, and advising.", "AwardID" -> "1500759", "Institution" -> Entity["NSFInstitution", "PurdueUniversity"], "Investigators" -> {Entity["NSFInvestigator", "FreydoonShahidi"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500759&HistoricalAwards=false"], "KeywordTally" -> {{"means", 5}, {"project", 5}, {"Artin", 4}, {"certain", 4}, {"laws", 4}, {"objects", 4}, {"reciprocity", 4}, {"complex", 3}, {"equality", 3}, {"factors", 3}, {"groups", 3}, {"L-functions", 3}, {"numbers", 3}, {"root", 3}, {"theory", 3}, {"analytic", 2}, {"approach", 2}, {"establishing", 2}, {"general", 2}, {"intertwining", 2}, {"Langlands", 2}, {"nature", 2}, {"presentations", 2}, {"preserving", 2}, {"Reciprocity", 2}, {"separate", 2}, {"sets", 2}, {"suggests", 2}}|>, "1500761" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: The Genomic Nature of Adaptation in Anolis lizards", "AwardEffectiveDate" -> DateObject[{2015, 5, 15}], "AwardExpirationDate" -> DateObject[{2016, 4, 30}], "AwardAmount" -> Quantity[19955, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010207", "ProgramOfficer" -> "Leslie Rissler", "Abstract" -> "Most of the biological diversity on Earth is thought to result from adaptive radiation, an evolutionary phenomenon where many new species are rapidly formed through colonization of and adaptation to new environments. The work of many researchers over the last fifty years has resulted in an emerging understanding of the broad-scale evolutionary patterns associated with adaptive radiation. Despite these advances, we have little understanding of the genetic processes that take place during adaptive radiation. For instance, it is not known how often new mutations are uniquely favored in one environment alone versus being beneficial to multiple species living in different habitats. This proposal addresses this gap in our knowledge using one of the most iconic examples of adaptive radiation, Anolis lizards from the West Indies. This research will focus on two Anolis species that reside on tree trunks?one living in a hot, dry environment, the other in a moist, cool forest. In a small area of the Dominican Republic, these different habitats are immediately adjacent to one another. Here, the two species interbreed and form hybrid offspring. These unique circumstances provide an opportunity to identify what gene variants are associated with adaptation to the two distinct environments and what variants are beneficial to both species.\n\nTo address the genomic nature of adaptation in Anolis lizards, the co-investigators will use next-generation sequencing technologies to collect transcriptome data from individuals of each species as well as hybrids. The genotypes derived from this sequencing will be used to perform genomic cline analyses, which identify parental alleles that are over- and underrepresented among hybrids. The results of genomic cline analyses will be combined with population genomic analyses to identify the frequency of global and local adaptations and provide a first insight into the microevolutionary processes associated with adaptive radiation.", "AwardID" -> "1500761", "Institution" -> Entity["NSFInstitution", "UniversityOfRochester"], "Investigators" -> {Entity["NSFInvestigator", "RichardGlor"], Entity["NSFInvestigator", "AnthonyGeneva"], Entity["NSFInvestigator", "DanielGarrigan"]}, "ProgramElements" -> {{"Code" -> "7378", "Text" -> "EVOLUTIONARY GENETICS"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500761&HistoricalAwards=false"], "KeywordTally" -> {{"adaptive", 5}, {"radiation", 5}, {"species", 5}, {"genomic", 4}, {"adaptation", 3}, {"analyses", 3}, {"Anolis", 3}, {"associated", 3}, {"identify", 3}, {"new", 3}, {"beneficial", 2}, {"cline", 2}, {"different", 2}, {"environment", 2}, {"environments", 2}, {"evolutionary", 2}, {"habitats", 2}, {"hybrids", 2}, {"living", 2}, {"lizards", 2}, {"processes", 2}, {"provide", 2}, {"sequencing", 2}, {"understanding", 2}, {"variants", 2}}|>, "1500771" -> <|"AwardTitle" -> "Free boundaries and extremal inequalities", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[124812, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "A free boundary is an interface between two materials like oil and water. Another example is the curve outlining the wake of a boat. Yet another is the interface between plasma and ordinary matter in a fusion reactor. Remarkably, the same mathematics of free boundaries that describes these physical phenomena can be used to design optimal shapes. For example, when one wants to enclose an oven or pipe with insulating material, there is a shape that is optimal in the sense that the sum of the cost of insulation and the cost due to heat loss is minimized. Moreover, even farther from physics, one can seek optimal ways to divide data sets into yes/no regions according to rules that minimize the errors, that is, false positive or false negative identifications or diagnoses. The overarching goal of this project is to reduce the complexity of the problem of searching for these optimal shapes. The expectation is that there are broad classes of situations in which the optimal divider (free boundary) resembles a straight line or plane at an appropriate scale. In those cases, one can be confident of finding a near optimal shape quickly. In addition to conducting his own research, the PI has served and will serve as faculty advisor for research projects by dozens of undergraduates and high school students in programs at MIT. Moreover, he has posted videos and lecture notes of a widely viewed single variable calculus course on MIT's Open Courseware site. He is currently working on an on-line course to be disseminated by MITx.\n\nFree boundaries arise as the interface between materials in which the materials retain some energy. Typically, space is divided into level sets of some quantity like temperature or pressure. In contrast, the interface represented by a minimal surface lives in an ambient space that is empty. Despite this difference between these two types of interfaces, there are profound connections between them. The main goal of this project is to show that interfaces and level sets of least energy for a wide variety of problems are as simple as possible. The PI proposes that the level sets of optimizers resemble parallel planes in that these surfaces are connected and cleanly separated. Usually, methods from the more developed theory of minimal surfaces have guided the study of free boundaries, but here ideas from the theory of free boundaries will guide the study of minimal surfaces. The proposal also gives a pathway to proving analogous simple behavior of level sets of the least energy Neumann eigenfunction for a convex symmetric domain. This would yield an important case of the longstanding ``hot spots'' conjecture of J. Rauch. A second project is to identify the cases of equality in the celebrated Alexandrov-Fenchel inequalities in convex geometry. The PI will use a geometric approach based on establishing new properties, of independent interest, of the Brenier (optimal transportation) mapping. A third project is aimed at developing a highly accurate description of localization of eigenfunctions and quantum tunneling, relevant to the design of LEDs.", "AwardID" -> "1500771", "Institution" -> Entity["NSFInstitution", "MassachusettsInstituteOfTechnology"], "Investigators" -> {Entity["NSFInvestigator", "DavidJerison"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500771&HistoricalAwards=false"], "KeywordTally" -> {{"optimal", 7}, {"free", 5}, {"sets", 5}, {"boundaries", 4}, {"interface", 4}, {"level", 4}, {"project", 4}, {"energy", 3}, {"materials", 3}, {"minimal", 3}, {"PI", 3}, {"surfaces", 3}, {"boundary", 2}, {"cases", 2}, {"convex", 2}, {"cost", 2}, {"course", 2}, {"design", 2}, {"example", 2}, {"false", 2}, {"goal", 2}, {"interfaces", 2}, {"like", 2}, {"Moreover", 2}, {"research", 2}, {"shape", 2}, {"shapes", 2}, {"simple", 2}, {"space", 2}, {"study", 2}, {"theory", 2}}|>, "1500774" -> <|"AwardTitle" -> "Connecting New Systematic Biologists Across Borders: A Workshop in Model-Based Phylogenetics at Evolution 2015", "AwardEffectiveDate" -> DateObject[{2015, 3, 1}], "AwardExpirationDate" -> DateObject[{2016, 12, 31}], "AwardAmount" -> Quantity[47608, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010206", "ProgramOfficer" -> "Simon Malcomber", "Abstract" -> "This award to University of Colorado, Boulder is made to support travel for twenty US graduate students, and three invited speakers from US institutions to a day-long workshop on model-based phylogenetics and phylogeography on the day prior to the Evolution meetings in Guarujo, Brazil (June 26, 2015). Model-based phylogenetic methods are growing at a staggering pace and now provide researchers with an opportunity to address research questions that were not possible before. This proposal is worthy of funding because it will allow U.S. researchers to learn about these new model-based phylogenetic methods first hand from several of the leading researchers in the field. The workshop is structured to provide an introduction to the theory behind the models followed by hands-on experience with the various software packages using real world data. The PIs and speakers have a strong track record of running successful workshops on similar topics demonstrating the feasibility of the proposed plan. \n\nThe award will support travel to the meeting and accommodation for twenty US graduate students, including members of under-represented groups. All workshop tutorials will be made publically available through a dedicated website and all presentations will be uploaded to YouTube after the meeting. 100 foreign graduate students, predominantly from South and Central America, will also attend the workshop enhancing opportunities for international scientific collaboration.", "AwardID" -> "1500774", "Institution" -> Entity["NSFInstitution", "UniversityOfColoradoAtBoulder"], "Investigators" -> {Entity["NSFInvestigator", "StaceySmith"], Entity["NSFInvestigator", "BryanCarstens"]}, "ProgramElements" -> {{"Code" -> "1171", "Text" -> "PHYLOGENETIC SYSTEMATICS"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500774&HistoricalAwards=false"], "KeywordTally" -> {{"workshop", 4}, {"graduate", 3}, {"researchers", 3}, {"students", 3}, {"award", 2}, {"meeting", 2}, {"methods", 2}, {"model-based", 2}, {"phylogenetic", 2}, {"provide", 2}, {"speakers", 2}, {"support", 2}, {"travel", 2}, {"twenty", 2}}|>, "1500779" -> <|"AwardTitle" -> "Linguistic and ethnographic sound recordings from early twentieth-century California: Optical scanning, digitization, and access", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "California has over 90 indigenous languages belonging to 21 different language families, and is linguistically more diverse than any area of its size in the western hemisphere. A hundred years ago, almost all California Native languages still had speakers; in most cases there were active speech communities using traditional narrative, oratory, ritual, teaching, and other speech practices in addition to rich song cultures. During the early decades of the twentieth century, beginning in 1901, Native people recorded songs and spoken texts on wax cylinders in collaboration with anthropologists and linguists at the University of California, Berkeley. The resulting collection of 2,713 cylinders contains over 100 hours of recordings in 78 languages, including about half of California's Native languages. For seven languages these are the only known sound recordings, and in many other cases they include unique speech practices and otherwise unknown stories and songs. Today, though fewer than half of California's indigenous languages have any first-language speakers (in almost all cases fewer than half a dozen), many Native communities have active language restoration programs and would welcome access to sound recordings made a century ago.\n\nThis project will apply new technology developed at the Lawrence Berkeley National Laboratory to create audio transfers of all wax cylinders at UC Berkeley. This involves optical restoration using a precision optical probe that creates a high-resolution profile of the cylinder surface; this profile can be formed into a three-dimensional digital image. An algorithm on a computer then processes the image to calculate the stylus motion and numerically extract the audio signal. The resulting audio transfers are superior to those produced invasively (with a physical stylus), and can even be created from broken cylinders. The entire cylinder collection will be scanned and digitally archived within a three-year window, in a collaboration involving the Hearst Museum of Anthropology (where the wax cylinder collection is housed), the University Library (where the scanning and digitization will be done), and the Department of Linguistics (which operates the California Language Archive, an online resource where the resulting audio files will be archived and accessible).", "AwardID" -> "1500779", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Berkeley"], "Investigators" -> {Entity["NSFInvestigator", "AndrewGarrett"], Entity["NSFInvestigator", "IraStuartJacknis"], Entity["NSFInvestigator", "ErikMitchell"]}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500779&HistoricalAwards=false"], "KeywordTally" -> {{"languages", 6}, {"audio", 4}, {"California", 4}, {"cylinders", 4}, {"Native", 4}, {"Berkeley", 3}, {"cases", 3}, {"collection", 3}, {"cylinder", 3}, {"half", 3}, {"recordings", 3}, {"resulting", 3}, {"speech", 3}, {"wax", 3}, {"active", 2}, {"archived", 2}, {"California's", 2}, {"century", 2}, {"collaboration", 2}, {"communities", 2}, {"fewer", 2}, {"image", 2}, {"indigenous", 2}, {"language", 2}, {"optical", 2}, {"practices", 2}, {"profile", 2}, {"restoration", 2}, {"songs", 2}, {"sound", 2}, {"speakers", 2}, {"stylus", 2}, {"transfers", 2}, {"University", 2}, {"using", 2}}|>, "1500790" -> <|"AwardTitle" -> "Combinatorial set theory", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[59305, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "The main focus of the proposal is the investigation of several types of infinite structure, using a range of mathematical tools. A secondary focus is the investigation of problems about very large finite structures, using certain infinite \"limit\" structures. Some of the problems to be studied are \"test questions\" intended to stimulate the development of new idea and methods.\n\nThe topics of the proposal are mostly concerned with large cardinals, ZFC combinatorics (particularly of singular cardinals) and forcing. They include forcing axioms for successors of singulars, various forms of the tree property, connections between compactness properties, PCF theory and universality numbers. The last section of the proposal is concerned with problems arising in Razborov's theory of flag algebras.", "AwardID" -> "1500790", "Institution" -> Entity["NSFInstitution", "Carnegie-MellonUniversity"], "Investigators" -> {Entity["NSFInvestigator", "JamesCummings"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500790&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 3}, {"proposal", 3}, {"cardinals", 2}, {"concerned", 2}, {"focus", 2}, {"forcing", 2}, {"infinite", 2}, {"investigation", 2}, {"large", 2}, {"structures", 2}, {"theory", 2}, {"using", 2}}|>, "1500796" -> <|"AwardTitle" -> "Sixth Symposium on Analysis and Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 1, 15}], "AwardExpirationDate" -> DateObject[{2015, 12, 31}], "AwardAmount" -> Quantity[35000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This award provides support for participants in the Sixth Symposium on Analysis and Partial Differential Equations, to be held at the Purdue University during June 1-4, 2015. The Symposium will bring together leading experts working in analysis, partial differential equations, and their applications, at different stages of their careers, to summarize the most recent progress in these topics, provide an opportunity to exchange ideas towards the solutions of open problems, and formulate and develop new directions and avenues of research. The Symposium will combine two short courses at an introductory level with more advanced lectures. This structure is designed to introduce prospective and young researchers to a larger mathematical community, and to help them establish new professional connections in their areas of interest. The mini-courses will encourage and enable students to participate in the more specialized parts of the Symposium and also other research conferences. \n\nThe Symposium will focus on recent developments in analysis and partial differential equations that are at the forefront of current research. The Symposium features two principal lecturers, each of whom will present four-hour mini-courses aimed at graduate students and recent doctoral degree recipients. Approximately ten invited speakers will deliver related one-hour lectures. In addition, approximately ten graduate students and recent doctoral degree recipients will present twenty-minute talks. The Symposium?s mini-courses are \"Free Boundaries and Minimal Surfaces,\" presented by David Jerison of MIT, and \"Extremum Problems for Elliptic Eigenvalues,\" by Fang-Hua Lin of the Courant Institute. More information on the symposium will be provided at the web page www.math.purdue.edu/~danielli.", "AwardID" -> "1500796", "Institution" -> Entity["NSFInstitution", "PurdueUniversity"], "Investigators" -> {Entity["NSFInvestigator", "DonatellaDanielli"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500796&HistoricalAwards=false"], "KeywordTally" -> {{"Symposium", 7}, {"recent", 4}, {"mini-courses", 3}, {"research", 3}, {"students", 3}, {"analysis", 2}, {"degree", 2}, {"differential", 2}, {"doctoral", 2}, {"equations", 2}, {"graduate", 2}, {"-hour", 2}, {"lectures", 2}, {"new", 2}, {"partial", 2}, {"present", 2}, {"recipients", 2}, {"ten", 2}}|>, "1500798" -> <|"AwardTitle" -> "Dissertation Research: Origin of the modern avian locomotor system across a neglected evolutionary interval: insight from new methods and new fossils", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2016, 6, 30}], "AwardAmount" -> Quantity[21203, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010206", "ProgramOfficer" -> "Simon Malcomber", "Abstract" -> "Despite the biological novelty of avian flight, little is known about what the most recent common ancestor of birds looked like, nor about how that ancestor flew. Using spectacular new fossil material, sophisticated imaging techniques, and rigorous statistical methods, this research will reconstruct the most likely anatomical and functional attributes of the most recent common ancestor of living birds, bringing us closer to understanding how modern birds and their flying ability came to be. Through museum exhibits, media exposure, and innovative online activities, this project has strong potential to educate both children and adults about evolutionary biology and paleontology.\n\nThe study will begin with allometric analysis of a comprehensive sampling of fossil taxa. Preliminary results from this analysis (based on >13,000 data points from extant birds) indicate a fundamental allometric division between extant flying and flightless birds. This division, based on the relationship between shoulder joint dimensions and body mass, enables, for the first time, the delineation of well-defined ?flying? and ?flightless? zones for morphology. This novel biomechanical ?test? of powered flying potential can easily be applied to Mesozoic fossils, and preliminary results indicate that the acquisition of a biomechanically favorable shoulder:body mass ratio, enabling powered flight, evolved considerably later in avian evolutionary history than is conventionally assumed. These results set the stage for a novel geometric analysis of Mesozoic stem bird postcrania, which will illustrate when the geometrically modern avian flight apparatus arose, and will shed light on the evolutionary dynamics of this deeply integrated morphological system. Next, the study will focus on the avian crown clade, and will generate the first ever three-dimensional in situ muscle and feather reconstructions of adult extant birds, which will facilitate the robust inference of flight muscle morphology for the most recent ancestor of extant birds. This will form the basis of range-of-motion simulations for the flight apparatus of two pivotal fossil stem birds, validated by data from diverse extant taxa. Together, the project outlined here will rigorously document and mechanically interpret one of the most important functional transitions in vertebrate evolutionary history?the acquisition of modern, powered flying ability in birds.", "AwardID" -> "1500798", "Institution" -> Entity["NSFInstitution", "YaleUniversity"], "Investigators" -> {Entity["NSFInvestigator", "Bhart-AnjanBhullar"], Entity["NSFInvestigator", "DanielField"]}, "ProgramElements" -> {{"Code" -> "1171", "Text" -> "PHYLOGENETIC SYSTEMATICS"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500798&HistoricalAwards=false"], "KeywordTally" -> {{"birds", 9}, {"extant", 5}, {"flight", 5}, {"flying", 5}, {"ancestor", 4}, {"avian", 4}, {"evolutionary", 4}, {"analysis", 3}, {"fossil", 3}, {"modern", 3}, {"powered", 3}, {"recent", 3}, {"results", 3}, {"ability", 2}, {"acquisition", 2}, {"allometric", 2}, {"apparatus", 2}, {"based", 2}, {"body", 2}, {"common", 2}, {"data", 2}, {"division", 2}, {"flightless", 2}, {"functional", 2}, {"history", 2}, {"indicate", 2}, {"mass", 2}, {"Mesozoic", 2}, {"morphology", 2}, {"muscle", 2}, {"novel", 2}, {"potential", 2}, {"project", 2}, {"shoulder", 2}, {"stem", 2}, {"study", 2}, {"taxa", 2}}|>, "1500800" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Innovation and constraint: the evolution of power-amplified feeding in syngnathiform fishes", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 5, 31}], "AwardAmount" -> Quantity[20290, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010206", "ProgramOfficer" -> "Simon Malcomber", "Abstract" -> "Syngnathiformes (seahorses, pipefishes, trumpetfish and relatives) are a group of fishes with unusual and novel modes of locomotion, reproduction, and feeding. Nearly all species are characterized by an elongated snout, which they rotate towards prey during feeding strikes. Recent research has shown that seahorses and pipefish are using power amplification to achieve extremely fast rotations, resulting in strikes that are among the fastest recorded for any fish (less than 2.5 milliseconds). This research will reconstruct the sequential evolutionary assembly of this mechanically extreme feeding mechanism and will investigate the consequences of this feeding mechanism on head shape diversity. The findings of this work will advance knowledge about how complex structure-function relationships evolve and influence subsequent structural evolution. The study will produce set of phylogenetic trees that reveal the evolutionary relationships among over 200 syngnathiform species. These will be a valuable resource and shared with other researchers to advance knowledge of the evolutionary history of this unique and unusual group of fishes. Other data and products from this research, including slow-motion videos, will engage a wide audience in the diversity of fish feeding strategies by incorporation into existing coursework at the University of California, Davis and through YouTube. In addition to forming an ambitious and integrative doctoral dissertation, this research will involve undergraduates interested in pursuing STEM related fields through hands-on training and experience. \n\nThis research will investigate the evolution of a mechanically extreme and complex feeding mechanism in syngnathiform fishes, beginning with the inference of a phylogeny using modern hybrid-enrichment (ultraconserved elements, UCEs) and next-generation sequencing technologies (Objective #1). Previous research has shown that seahorses and pipefish use power amplification to rotate their head towards prey faster than would be possible by direct muscle activation, and it has been proposed that this mechanism relies on a unique pivot joint in the skull. A combination of morphological and functional approaches including high-speed video, biomechanical modeling, and micro-CT scanning will be used to characterize and compare the feeding functional morphology of lineages related to seahorses and pipefish (Objective #2). The phylogeny from Objective #1 will be used to reconstruct the evolutionary history of the structural and functional changes necessary for power-amplified feeding in syngnathiform fishes and to test hypotheses about how the possession of this specialized mechanism has influenced the evolution of head shape in syngnathiforms (Objective #3). Models of continuous character evolution will to be fit to craniofacial shape data and compared in the software program OUwie to test the hypothesis that the possession of power amplification exerts strong stabilizing selection on craniofacial morphology. While the literature focuses on innovations that increase diversity, this work incorporates a model-testing approach to determine whether this novel feeding mechanism may constrain morphological diversification at macroevolutionary timescales.", "AwardID" -> "1500800", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Davis"], "Investigators" -> {Entity["NSFInvestigator", "PeterWainwright"], Entity["NSFInvestigator", "SarahLongo"]}, "ProgramElements" -> {{"Code" -> "1171", "Text" -> "PHYLOGENETIC SYSTEMATICS"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500800&HistoricalAwards=false"], "KeywordTally" -> {{"feeding", 9}, {"mechanism", 6}, {"research", 6}, {"evolution", 4}, {"evolutionary", 4}, {"fishes", 4}, {"Objective", 4}, {"seahorses", 4}, {"amplification", 3}, {"diversity", 3}, {"functional", 3}, {"head", 3}, {"pipefish", 3}, {"power", 3}, {"shape", 3}, {"syngnathiform", 3}, {"advance", 2}, {"complex", 2}, {"craniofacial", 2}, {"data", 2}, {"extreme", 2}, {"fish", 2}, {"group", 2}, {"history", 2}, {"including", 2}, {"investigate", 2}, {"knowledge", 2}, {"mechanically", 2}, {"morphological", 2}, {"morphology", 2}, {"novel", 2}, {"phylogeny", 2}, {"possession", 2}, {"prey", 2}, {"reconstruct", 2}, {"related", 2}, {"relationships", 2}, {"rotate", 2}, {"shown", 2}, {"species", 2}, {"strikes", 2}, {"structural", 2}, {"test", 2}, {"towards", 2}, {"unique", 2}, {"unusual", 2}, {"used", 2}, {"using", 2}, {"work", 2}}|>, "1500802" -> <|"AwardTitle" -> "Doctoral Dissertation Research: Yazgulyami Syllable Structure [yah]", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2017, 7, 31}], "AwardAmount" -> Quantity[17993, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Yazgulyami is a severely endangered Pamiri (Southeastern Iranian) language, spoken primarily along the Yazgulyam River in the mountains of eastern Tajikistan. Recent history has seen the encroachment of Tajik culture and the concomitant death of several neighboring Pamiri languages. This project has two primary aims, one descriptive and one theoretical. Firstly, this work will create a living language corpus of Yazgulyami speech composed of annotated audio and video recordings alongside a multilingual dictionary. Additionally, this research will examine and formally model the syllabification of consonant clusters. In Yazgulyami, up to three consonants may begin a word. Previous work on the language suggests that these clusters may be polysyllabic, creating syllables composed entirely on consonants, like pt and zv. If this is the case, Yazgulyami is one of the very few languages that allow vowel-less syllables. Languages like this raise the question of what makes up a syllable, an important empirical question. \n\nIn pursuit of these two goals, speech data will be collected from a Yazgulyami village in eastern Tajikistan. A variety of stories, conversations, and songs will be recorded, including poetry and language games, which will supplement acoustic analysis of word-initial syllables. Poetry and language games (e.g. Pig Latin) often refer to syllables, giving the researcher an opportunity to access native speaker conceptions of syllable boundaries. Empirical findings from this study will be formalized according to contemporary phonetic and phonological theory, addressing the underlying as well as surface realization of these syllabic structures.\n\nThis project will provide a needed documentation of a swiftly changing language in an understudied region of the world. Moreover, the project will enable a graduate student to collaborate with an endangered speech community on the description of their language while producing a theoretical analysis of a rarely attested sound pattern.", "AwardID" -> "1500802", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-SanDiego"], "Investigators" -> {Entity["NSFInvestigator", "SharonRose"], Entity["NSFInvestigator", "AdamMcCollum"]}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500802&HistoricalAwards=false"], "KeywordTally" -> {{"language", 7}, {"Yazgulyami", 5}, {"syllables", 4}, {"project", 3}, {"speech", 3}, {"analysis", 2}, {"clusters", 2}, {"composed", 2}, {"consonants", 2}, {"eastern", 2}, {"endangered", 2}, {"games", 2}, {"languages", 2}, {"like", 2}, {"Pamiri", 2}, {"question", 2}, {"syllable", 2}, {"Tajikistan", 2}, {"theoretical", 2}, {"work", 2}}|>, "1500806" -> <|"AwardTitle" -> "Noncommutative Geometry and Elliptic Special Functions", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[90000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "Historically, the study of \"special functions\" originated in the fact that quite a few functions of interest in applications turned out to be members of a single family, the hypergeometric functions; more recently, the Painleve transcendents have also begun to play a significant role in applications. Under previous grants, the investigator constructed and studied so-called \"elliptic\" analogues of these functions (a significant generalization that includes most of the generalized hypergeometric functions and generalized Painleve transcendents in the literature), as well as their implications for the more classical special functions. The current project continues this work, and aims to provide a more solid conceptual framework by relating elliptic special functions to noncommutative algebraic geometry, which is a relatively recent variant of algebraic geometry, one of the fundamental disciplines within mathematics.\n\nThis connection is based on a new construction of noncommutative rational surfaces in terms of difference operators on elliptic curves (giving a discrete analogue of D-module theory), giving rise to a (functorial) relation between linear elliptic difference equations and sheaves on the noncommutative surfaces. The Painleve equations (and generalizations) are most naturally interpreted as flows in moduli spaces of differential equations, so one expects their elliptic analogues to be related to moduli spaces of difference equations, and thus to moduli spaces of sheaves. In particular, the investigator expects to be able to leverage the existing literature on noncommutative algebraic geometry to understand the structure of such moduli spaces, as well as various natural maps between them (e.g., twisting by line bundles). In addition, since the new construction of highly-blown-up noncommutative rational surfaces is considerably more concrete than the previously existing constructions, the investigator expects the project to contribute significantly to our understanding of such surfaces in their own right (as well as their derived categories). Finally, several of the difference operators that arise in the construction are univariate analogues of operators that appeared in earlier work of the investigator on elliptic analogues of Macdonald-Koornwinder polynomials; this leads to a multivariate analogue of the construction with connections not just to those elliptic analogues but also to certain integrable systems and to an elliptic analogue of the \"double affine Hecke algebras\" of Cherednik.", "AwardID" -> "1500806", "Institution" -> Entity["NSFInstitution", "CaliforniaInstituteOfTechnology"], "Investigators" -> {Entity["NSFInvestigator", "EricRains"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500806&HistoricalAwards=false"], "KeywordTally" -> {{"elliptic", 8}, {"functions", 7}, {"analogues", 5}, {"noncommutative", 5}, {"construction", 4}, {"difference", 4}, {"equations", 4}, {"investigator", 4}, {"moduli", 4}, {"spaces", 4}, {"surfaces", 4}, {"algebraic", 3}, {"analogue", 3}, {"expects", 3}, {"geometry", 3}, {"operators", 3}, {"Painleve", 3}, {"special", 3}, {"applications", 2}, {"existing", 2}, {"generalized", 2}, {"giving", 2}, {"hypergeometric", 2}, {"literature", 2}, {"new", 2}, {"project", 2}, {"rational", 2}, {"sheaves", 2}, {"significant", 2}, {"transcendents", 2}, {"work", 2}}|>, "1500811" -> <|"AwardTitle" -> "Doctoral Dissertation Research: Using Ethnographic Methods to Document the Garifuna Language", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2016, 5, 31}], "AwardAmount" -> Quantity[15119, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Speaker responses about language use in interview settings are often skewed towards formal and prescriptively sanctioned norms. By collecting and analyzing video and audio recordings of everyday conversations, narratives, and routinized speech events including ancestor rituals, Alison Broach under the direction of Eve Danziger of the University of Virginia will create a corpus naturalistic Garifuna [cab] speech. The data samples in the resulting corpus will have been only minimally affected by the data collection process. \n\nGarifuna is an Arawakan language spoken in several Central American countries and on the Caribbean island of St. Vincent. Broach will document the Guatemalan variety about which little has been written. Garifuna is of interest because of its unique historical origins through which it has acquired both Carib and West African features. Documenting Garifuna using both state-of-the-art ethnographic and language documentation methods, Broach will study in depth the morphological and lexical borrowings into Garifuna from Spanish and French, languages with which Garifuna is in close contact. This data will then lead to an analysis of how Garifuna has changed over time, especially as Spanish and English replace Garifuna as the language of choice for member of the speech community. Results will also inform ongoing Garifuna language revitalization efforts. \n\nGarifuna data will be archived at the Archive of the Indigenous Languages of Latin America and at LIBRA, an online open access repository for University of Virginia scholars.", "AwardID" -> "1500811", "Institution" -> Entity["NSFInstitution", "UniversityOfVirginiaMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "EveDanziger"], Entity["NSFInvestigator", "AlisonBroach"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500811&HistoricalAwards=false"], "KeywordTally" -> {{"Garifuna", 8}, {"language", 5}, {"data", 4}, {"Broach", 3}, {"speech", 3}, {"br/>

Garifuna", 2}, {"corpus", 2}, {"Spanish", 2}, {"University", 2}, {"Virginia", 2}}|>, "1500812" -> <|"AwardTitle" -> "Qualitative Properties of Eigenfunctions for some Selfadjoint and Non-selfadjoint partial differential equations", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[120000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This project considers eigenfunctions, which are objects that give information about, for example, the vibrations of a ringing drum head. In other contexts, these eigenfunctions can describe, for example, how fluids mix on extremely small length scales, with potential applications to improved efficiency in medical drug delivery and dialysis. These eigenfunctions are fundamental building blocks to understand problems in mathematics, physics, chemistry, and even biomedical engineering. It is precisely these important fundamental connections between the proposed research and STEM subjects that makes this research have broader significance within the larger context of the STEM areas. The PI has been developing simple, instructional model problems related to most of his research for students and younger researchers. \n\nThis project concerns research in the deep relationships between solutions to partial differential equations, differential geometry, dynamical systems, and mathematical physics. These different areas of mathematics are often tied together by problems in spectral theory and microlocal analysis; that is, problems concerned with eigenvalues, eigenfunctions, phase space localization, and the generalizations thereof. The research in this proposal is divided between selfadjoint and non-selfadjoint eigenfunction problems. The study of the behaviour of solutions to partial differential equations has a rich connection to the underlying geometry and classical phase space dynamics. For example, it is well known that eigenfunctions tend to concentrate along geodesics. If there are isolated periodic geodesics, one might expect a subsequence of eigenfunctions to concentrate along such geodesics. Understanding the rate of concentration is an extremely important question in quantum chaos. On the other hand, if the geodesic flow is sufficiently chaotic, one might expect the eigenfunctions to be equidistributed in phase space. It is important to investigate how robust these phenomena are, through phase space estimates, restriction estimates, and perturbations. For example, in the chaotic case, the PI and his collaborators are working to understand restrictions of eigenfunctions to hypersurfaces. With mild geometric assumptions on a hypersurface, they conjecture the mass of such restrictions is bounded above and below, independent of the eigenvalue. The methods of investigation will introduce new microlocal energy techniques, demonstrating how to generalize a problem, previously only understood on arithmetic surfaces using number theory, to very general geometric situations. Some properties of eigenfunctions tend to be stable under small complex perturbations, which means one can also understand some non-selfadjoint problems. For non-selfadjoint problems with larger imaginary component, perturbation techniques are no longer strictly valid. The PI is working to develop a general theory of geometric control adapted to degenerate advection-diffusion type equations of any order. This has straightforward applications to the Fokker-Planck equation and similar equations from statistical mechanics. This theory also has applications to certain models in theoretic micro-fluidics, with potential applications to efficient geometrically localized drug delivery and dialysis.", "AwardID" -> "1500812", "Institution" -> Entity["NSFInstitution", "UniversityOfNorthCarolinaAtChapelHill"], "Investigators" -> {Entity["NSFInvestigator", "HansChristianson"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500812&HistoricalAwards=false"], "KeywordTally" -> {{"eigenfunctions", 9}, {"problems", 7}, {"research", 5}, {"applications", 4}, {"equations", 4}, {"example", 4}, {"phase", 4}, {"space", 4}, {"theory", 4}, {"differential", 3}, {"geodesics", 3}, {"geometric", 3}, {"important", 3}, {"non-selfadjoint", 3}, {"PI", 3}, {"understand", 3}, {"areas", 2}, {"chaotic", 2}, {"concentrate", 2}, {"delivery", 2}, {"dialysis", 2}, {"drug", 2}, {"estimates", 2}, {"expect", 2}, {"extremely", 2}, {"fundamental", 2}, {"general", 2}, {"geometry", 2}, {"larger", 2}, {"mathematics", 2}, {"microlocal", 2}, {"partial", 2}, {"perturbations", 2}, {"physics", 2}, {"potential", 2}, {"project", 2}, {"restrictions", 2}, {"small", 2}, {"solutions", 2}, {"STEM", 2}, {"techniques", 2}, {"tend", 2}, {"working", 2}}|>, "1500815" -> <|"AwardTitle" -> "EAGER: Rapid Screening and Identification of Organisms which Hyper-Accumulate Metals", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2017, 8, 31}], "AwardAmount" -> Quantity[200000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07020000", "ProgramOfficer" -> "Carole Read", "Abstract" -> "1500815\nSrivastava\nUniversity of Idaho\n\nRare earth elements (REE) are considered critical materials because of their essential usage in a variety of business sectors and their potential for supply shortages and scarcity. Recovery of REE from waste streams and end-of-life products is an attractive technology, however separation of REE from these materials can be costly and involve toxic and hazardous chemicals. Microorganisms have the capacity to selectively accumulate and fractionate metals including REE but have not been deployed as a separation technology for REE. The PI proposes to develop a high risk high payoff platform technology based on microfluidic separation using dielectrophoresis (DEP). The proposed work is anticipated to transform the screening of biomaterials by providing a highly adaptable means for high-throughput screening of superior performing biomaterials. \n\nThe proposed work will be accomplished through 1) utilizing computational fluid dynamics to design and simulate a variety of DEP microdevices as a means for separation of OHMs and, 2) construction and validation of the microdevice using two very different model microorganisms, Acidithiobacillus ferrooxidans and Cupriavidus necator. \n\nDevelopment of a rapid screening tool for identification and separation of these high performing organisms would significantly enhance and accelerate screening and development of microorganisms used in biosorption of all types, not just specific to metals; providing a greener and potentially more cost effective technological solution to separation challenges.", "AwardID" -> "1500815", "Institution" -> Entity["NSFInstitution", "UniversityOfIdaho"], "Investigators" -> {Entity["NSFInvestigator", "SoumyaSrivastava"], Entity["NSFInvestigator", "JamesMoberly"]}, "ProgramElements" -> {{"Code" -> "1417", "Text" -> "CHEMICAL & BIOLOGICAL SEPAR"}}, "ProgramReferences" -> {{"Code" -> "136E", "Text" -> "Chemical Separation Processes"}, {"Code" -> "7916", "Text" -> "EAGER"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Chem, Bioeng, Env, & Transp Sys", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500815&HistoricalAwards=false"], "KeywordTally" -> {{"separation", 6}, {"REE", 5}, {"screening", 4}, {"high", 3}, {"technology", 3}, {"biomaterials", 2}, {"DEP", 2}, {"materials", 2}, {"means", 2}, {"metals", 2}, {"microorganisms", 2}, {"performing", 2}, {"proposed", 2}, {"providing", 2}, {"using", 2}, {"variety", 2}, {"work", 2}}|>, "1500817" -> <|"AwardTitle" -> "Elliptic Boundary Problems and Evolution Equations in Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[180000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "In this project the principal investigator will tackle problems in two areas in partial differential equations. The first involves equations for functions that vary with space but not with time. Such stationary problems model many physical systems in equilibrium, from static electric fields to configurations of elastic bodies, and also arise in fundamental investigations in mathematical analysis, including potential theory and analytic function theory. Problems of this type often involve unknown functions defined on bounded regions. One goal of this project is to extend our knowledge of how to handle such problems when the boundaries are quite rough. The second area involves evolution equations, for functions that vary with time. Core classes of interest in this project include equations for wave motion, both for classical waves and variants, such as Schrodinger equations and Dirac equations, whose origins lie in the motions of atoms.\n\nThis project will develop tools to advance the study of elliptic systems on domains with uniformly rectifiable boundary, which is essentially the maximal class of domains on which one can use singular integral operator techniques. One class of problems that will be tackled consists of Riemann-Hilbert type problems. These were first studied on planar domains, with piecewise smooth interfaces. This project will develop higher dimensional versions of Riemann-Hilbert problems, on domains with uniformly rectifiable interfaces. A related study will involve a development of the index theory of Toeplitz operators on such rough domains. The other major part of this project concerns evolution equations. Specific problems to be tackled include studies of wave decay, via various mechanisms, some related to the formation of harmonics on stringed instruments, but in a higher dimensional context. In addition, wave decay problems will be considered on domains with rough geometry, including cases where the main geometrical hypothesis is a lower bound on the Ricci tensor, and the challenge is to develop a theory of geometrical optics in this setting.", "AwardID" -> "1500817", "Institution" -> Entity["NSFInstitution", "UniversityOfNorthCarolinaAtChapelHill"], "Investigators" -> {Entity["NSFInvestigator", "MichaelTaylor::36x47"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500817&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 8}, {"equations", 7}, {"domains", 6}, {"project", 6}, {"theory", 4}, {"develop", 3}, {"functions", 3}, {"rough", 3}, {"wave", 3}, {"class", 2}, {"decay", 2}, {"dimensional", 2}, {"evolution", 2}, {"geometrical", 2}, {"higher", 2}, {"include", 2}, {"including", 2}, {"interfaces", 2}, {"involve", 2}, {"involves", 2}, {"rectifiable", 2}, {"related", 2}, {"Riemann-Hilbert", 2}, {"study", 2}, {"systems", 2}, {"tackled", 2}, {"time", 2}, {"type", 2}, {"uniformly", 2}, {"vary", 2}}|>, "1500818" -> <|"AwardTitle" -> "Reduced Order Modeling for Gravitational Waves", "AwardEffectiveDate" -> DateObject[{2014, 9, 3}], "AwardExpirationDate" -> DateObject[{2016, 8, 31}], "AwardAmount" -> Quantity[258942, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03010000", "ProgramOfficer" -> "Bogdan Mihaila", "Abstract" -> "The structure of the eight-dimensional parameter space for gravitational waves produced by binary black hole mergers is largely unknown. For each parameter value, each solution is found from numerically solving Einstein's equations and involves time intensive large-scale simulations. Hence, it is prohibitively expensive to explore the parameter space with traditional methods, which ultimately limits progress in gravitational waves physics and presents an important scientific challenge for the experimental program at the Laser Interferometer Gravitational-Wave Observatory (LIGO). In this project, new reduced-order modeling techniques will be developed for accurately representing solutions of parameterized problems that are expensive to solve for numerically, specifically in the context of gravitational waves from black hole binary mergers. \n\nThe results of this research project will enable the scientific community to make significant progress in the ability to map the continuum of gravitational waves from compact binary coalescence for gravitational wave detection purposes. It is expected the methods developed in this proposal will be useful for a broad range of other disciplines involving parameterized problems and expensive large-scale numerical solutions. The project involves significant contributions from two post-doctoral fellows, whose future careers will benefit from performing creative research at the forefront of an important scientific investigation.", "AwardID" -> "1500818", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-SanDiego"], "Investigators" -> {Entity["NSFInvestigator", "ManuelTiglio"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Physics", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500818&HistoricalAwards=false"], "KeywordTally" -> {{"gravitational", 5}, {"waves", 4}, {"binary", 3}, {"expensive", 3}, {"parameter", 3}, {"project", 3}, {"scientific", 3}, {"black", 2}, {"developed", 2}, {"hole", 2}, {"important", 2}, {"involves", 2}, {"large-scale", 2}, {"mergers", 2}, {"methods", 2}, {"numerically", 2}, {"parameterized", 2}, {"problems", 2}, {"progress", 2}, {"research", 2}, {"significant", 2}, {"solutions", 2}, {"space", 2}}|>, "1500820" -> <|"AwardTitle" -> "Conference on Algebraic, Enumerative and Topological Combinatorics", "AwardEffectiveDate" -> DateObject[{2015, 1, 1}], "AwardExpirationDate" -> DateObject[{2015, 12, 31}], "AwardAmount" -> Quantity[24500, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "From January fifth through January ninth of 2015, ``A Conference on Algebraic, Topological and Enumerative Combinatorics\" will be held at the University of Miami in Coral Gables, Florida. This conference will provide an opportunity for established experts and early career mathematicians to share ideas and results in the field of algebraic, enumerative and topological combinatorics. Combinatorics is the study of discrete, usually finite, mathematical structures. Examples of such structures are networks, such as the internet, phone systems and transportation systems. While finite structures are in principle easy to understand through exhaustive examination, this becomes practically impossible once the structures become too large. Thus more theoretical approaches are necessary. Practitioners in the field bring to bear techniques from various areas of mathematics that involve abstraction beyond what one might expect given the nature of the problems at hand.\n\nThe conference will feature talks on topics at the forefront of current research in the field. Among the likely topics of discussion both in talks and informal discussions are connections between combinatorics and various other areas, including algebraic geometry, topology, commutative algebra, representation theory and probability. Further information on the conference can be found at the conference website\n\nhttp://www.math.miami.edu/~galloway/wachsfest.html", "AwardID" -> "1500820", "Institution" -> Entity["NSFInstitution", "WashingtonUniversity"], "Investigators" -> {Entity["NSFInvestigator", "JohnShareshian"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500820&HistoricalAwards=false"], "KeywordTally" -> {{"conference", 4}, {"structures", 4}, {"field", 3}, {"algebraic", 2}, {"areas", 2}, {"combinatorics", 2}, {"Combinatorics", 2}, {"finite", 2}, {"January", 2}, {"systems", 2}, {"talks", 2}, {"topics", 2}, {"various", 2}}|>, "1500821" -> <|"AwardTitle" -> "Laplacian growth, Schwarz reflection, and random normal matrices", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[122012, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "Laplacian growth (LG) is one of the most important types of dynamics at the boundary between two objects. For example, LG arises naturally in the study of certain problems involving a moving boundary. As a growth process, LG is widely recognized as a model for the formation of various universal patterns observed in physics and natural sciences such as the growth of bacterial colonies. A new exiting development in this classical area of mathematical physics was the recent discovery of the fact that on the microscopic level, the mechanism of LG is very closely related to the behavior of particles in plasma ensembles. Plasma is one of the four fundamental states of matter. A common form of plasma is seen in neon signs and in fact plasma is the most common state of matter in the universe. These plasma ensembles are described in terms of mathematical objects call random matrices that have complex eigenvalues. The relation of LG and random matrices has been intensively studied on the physical level but many fundamental problems remain open on the mathematical side. The PI, Nikolai Makarov, will focus on several such problems. \n\nThe main topics and goals of the study will be the following: the proof of the convergence of rescaled point processes and the description of the universality laws for various types of boundary points in the random normal matrix model (RNM); the proof of the laminarity of Hele-Shaw flows and the rigorous derivation of their integrability properties;the analysis of the dynamics of the Schwarz reflections associated with algebraic droplets in the RNM model. To achieve these goals, the PI will bring together tools and ideas from various areas of mathematics (complex analysis, conformal dynamics, probability theory) and theoretical physics (conformal field theory, non-equilibrium growth phenomenon, disordered systems). The educational component of the project will be the development of new graduate courses and organization of scientific workshops and conferences. The project will provide research and training opportunities for graduate students and postdocs.", "AwardID" -> "1500821", "Institution" -> Entity["NSFInstitution", "CaliforniaInstituteOfTechnology"], "Investigators" -> {Entity["NSFInvestigator", "NikolaiMakarov"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500821&HistoricalAwards=false"], "KeywordTally" -> {{"LG", 5}, {"growth", 4}, {"plasma", 4}, {"boundary", 3}, {"dynamics", 3}, {"mathematical", 3}, {"model", 3}, {"physics", 3}, {"problems", 3}, {"random", 3}, {"various", 3}, {"analysis", 2}, {"common", 2}, {"complex", 2}, {"conformal", 2}, {"development", 2}, {"ensembles", 2}, {"fact", 2}, {"fundamental", 2}, {"goals", 2}, {"graduate", 2}, {"level", 2}, {"matrices", 2}, {"matter", 2}, {"new", 2}, {"objects", 2}, {"PI", 2}, {"project", 2}, {"proof", 2}, {"RNM", 2}, {"study", 2}, {"theory", 2}, {"types", 2}}|>, "1500823" -> <|"AwardTitle" -> "K-theory of operator algebras and invariants of elliptic operators", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[120000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "In real life, one seeks to understand objects in the universe by studying various characteristic quantities associated with them, such as shape, size, temperature, and so on. These characteristics allow one to distinguish one object from another. Some characteristics may change drastically under the influence of very small external forces, and some remain resistant to change under such forces. The former are unstable and usually difficult to measure, while the latter are more stable and easier to detect, hence much more useful. In mathematics, those stable characteristics are called invariants. They provide some of the most fundamental tools in almost all branches of mathematics. In this project, the principal investigator will study a certain class of invariants of differential equations and apply them to study problems in classical geometry and topology. \n\nIndex theoretical invariants of elliptic operators are important for understanding the geometry of their underlying spaces. The famous Atiyah-Singer index theorem and its noncommutative geometric generalizations have many applications to geometry and topology. All these index theoretical invariants live naturally in the K-theory of certain operator algebras. The principal investigator will use methods developed in the studies of K-theory of operator algebras to investigate various invariants of elliptic operators on manifolds and spaces with singularities. In particular, he is interested in secondary invariants such as the higher rho invariant. The principal investigator proposes to use these secondary invariants to study the structure group of a closed topological manifold and the homotopy groups of the space of positive scalar curvature metrics on a given manifold. The principal investigator also plans to explore the connections of these problems to the Novikov conjecture and the Baum-Connes conjecture.", "AwardID" -> "1500823", "Institution" -> Entity["NSFInstitution", "TexasA&MUniversityMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "ZhizhangXie"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500823&HistoricalAwards=false"], "KeywordTally" -> {{"invariants", 7}, {"investigator", 4}, {"principal", 4}, {"characteristics", 3}, {"geometry", 3}, {"study", 3}, {"algebras", 2}, {"certain", 2}, {"change", 2}, {"conjecture", 2}, {"elliptic", 2}, {"forces", 2}, {"index", 2}, {"K-theory", 2}, {"manifold", 2}, {"mathematics", 2}, {"operator", 2}, {"operators", 2}, {"problems", 2}, {"secondary", 2}, {"spaces", 2}, {"stable", 2}, {"theoretical", 2}, {"topology", 2}, {"use", 2}, {"various", 2}}|>, "1500824" -> <|"AwardTitle" -> "Multi-disciplinary Conference Investigating Tlingit Indigenous Place Names, Language and History", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2016, 7, 31}], "AwardAmount" -> Quantity[50000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Insights into language are enriched through cross-disciplinary investigation. The Indigenous Place Names, Language, and History conference will bring together experts in biology, traditional ecological knowledge, archaeology, linguistics, museum studies, cultural anthropology, education, ethnohistory, art, music, and indigenous law to share information from many perspectives on Tlingit (tli) language and culture. In addition to social scientists and humanities experts, the conference will include equal participation and presentations from Tlingit speakers and other tradition bearers who hold keys to contextualize linguistic and cultural findings. Under the direction of Alice Taff of Tlingit Readers, Incorporated, this Clan conference will generate knowledge on place names from coastal Southeastern Alaska from Yakutat south to Ketchikan. \n\nConference proceedings and presentations will be archived at the SeaAlaska Heritage Institute, Alaska State Library, and clanconference.org websites. The session will be available for viewing at clanconference.org.", "AwardID" -> "1500824", "Institution" -> Entity["NSFInstitution", "TlingitReaders,Inc."], "Investigators" -> {Entity["NSFInvestigator", "AliceTaff"]}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500824&HistoricalAwards=false"], "KeywordTally" -> {{"conference", 3}, {"Tlingit", 3}, {"Alaska", 2}, {"clanconference.org", 2}, {"cultural", 2}, {"experts", 2}, {"knowledge", 2}, {"language", 2}, {"presentations", 2}}|>, "1500829" -> <|"AwardTitle" -> "Nonlinear partial differential equations and continuum limits for large discrete sorting problems", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2017, 6, 30}], "AwardAmount" -> Quantity[76362, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The goal of this project is to study algorithms for sorting large amounts of high-dimensional data. Sorting, or ordering, data is one of the most fundamental problems in computational science, and in today's data-driven world, there is a need to develop new algorithms and tools for handling massive amounts of data in novel ways. Many sorting algorithms are computationally intensive, but have a highly predictable structure when applied to very large amounts of data. A deep mathematical understanding of this structure will lead to new insights that have the potential to significantly improve performance. Applications of sorting are ubiquitous in science and engineering, and include the analysis of DNA sequences, sorting of hits in web searches, and fingerprint identification. A significant improvement in any sorting algorithm would have a broad impact on many fields of science and engineering. \n\nThis project will study two algorithms for sorting multivariate data: non-dominated sorting, and convex hull ordering. Non-dominated sorting is fundamental in multi-objective optimization, which is commonly used in scientific and engineering contexts. It has recently been shown that non-dominated sorting of random points in Euclidean space has a continuum limit that corresponds to solving a Hamilton-Jacobi equation. The first objective of this project is to study the regularity of viscosity solutions of this Hamilton-Jacobi equation, and to develop highly accurate numerical schemes for approximating its solution. The second, and main objective, is to study convex hull ordering, which is widely used in robust statistics. It is conjectured that convex hull ordering has a continuum limit that corresponds to affine invariant curvature motion. This project aims to study, and prove rigorously, this conjectured continuum limit. This result provides an asymptotic distributional theory for convex hull ordering, which is an open problem in robust statistics. Another goal of this project is to exploit this continuum limit to develop a fast algorithm for approximate convex hull ordering that can handle massive amounts of data.", "AwardID" -> "1500829", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Berkeley"], "Investigators" -> {Entity["NSFInvestigator", "JeffreyCalder"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500829&HistoricalAwards=false"], "KeywordTally" -> {{"sorting", 9}, {"data", 6}, {"ordering", 6}, {"convex", 5}, {"hull", 5}, {"project", 5}, {"study", 5}, {"algorithms", 4}, {"amounts", 4}, {"continuum", 4}, {"limit", 4}, {"develop", 3}, {"engineering", 3}, {"science", 3}, {"algorithm", 2}, {"conjectured", 2}, {"corresponds", 2}, {"equation", 2}, {"fundamental", 2}, {"goal", 2}, {"Hamilton-Jacobi", 2}, {"highly", 2}, {"large", 2}, {"massive", 2}, {"new", 2}, {"non-dominated", 2}, {"objective", 2}, {"robust", 2}, {"statistics", 2}, {"structure", 2}, {"used", 2}}|>, "1500832" -> <|"AwardTitle" -> "Multivariate Hypergeometric Functions: Combinatorics and Algebra", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[150000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "Hypergeometric functions in one variable are fundamental objects of widespread use in mathematics, science, and engineering. Hypergeometric functions in several variables share this importance. For instance, polynomial equations of degrees five or higher cannot be solved in terms of radicals, but they can always be solved using multivariate hypergeometric functions, regardless of the degree. Working in several variables, however, presents substantial challenges. This project seeks to overcome these challenges by developing new combinatorial and algebraic techniques. An important attribute of all hypergeometric functions and differential equations is that they depend on parameters; varying the parameters can cause substantial changes, and in most cases, neither these effects nor the mechanisms that control them are completely understood. The specific questions addressed in this project involve the investigation of the parametric behavior of hypergeometric functions and differential equations.\n\nIn the late twentieth century, Gelfand, Graev, Kapranov, and Zelevinsky introduced a generalized theory of hypergeometric functions and differential equations based on toric varieties. Powerful algebro-combinatorial tools of independent interest were developed by these authors in the hypergeometric context, which have provided vast and elegant generalizations of some very classical statements about hypergeometric functions in one variable. The goal of this project is to use techniques drawn from polyhedral geometry, commutative algebra, D-module theory and complex analysis to study these hypergeometric functions and differential equations. The development of new tools for this study also motivates and inspires specific projects within combinatorial commutative algebra. Another major theme is to use hypergeometric tools and intuition to obtain results beyond the hypergeometric world.", "AwardID" -> "1500832", "Institution" -> Entity["NSFInstitution", "TexasA&MUniversityMainCampus"], "Investigators" -> {Entity["NSFInvestigator", "LauraMatusevich"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500832&HistoricalAwards=false"], "KeywordTally" -> {{"hypergeometric", 9}, {"functions", 8}, {"differential", 4}, {"equations", 4}, {"project", 3}, {"tools", 3}, {"use", 3}, {"algebra", 2}, {"challenges", 2}, {"combinatorial", 2}, {"commutative", 2}, {"Hypergeometric", 2}, {"new", 2}, {"parameters", 2}, {"solved", 2}, {"specific", 2}, {"study", 2}, {"substantial", 2}, {"techniques", 2}, {"theory", 2}, {"variable", 2}, {"variables", 2}}|>, "1500834" -> <|"AwardTitle" -> "Algebraic, Combinatorial, and Analytic Applications of Symmetric Functions", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[130000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "From the lattice structure of crystals, to states of matter, to matrices and differential operators, the traits of systems and their evolution are classified by symmetries. Algebraic combinatorics studies symmetries via their manifestations in well-known discrete objects like graphs, permutations, and partitions. Its methods have successfully solved problems in other sciences such as physics, computer sciences, and biology. This project concerns the application of algebraic combinatorics, in particular its subfield the theory of symmetric functions, to solve such problems. \n\nThis project is centered around the tools used, namely, the theory of symmetric functions and the associated combinatorics. Various complexity problems in representation theory concern the computation of certain structure constants and multiplicities that are expressible via the Kronecker and plethystic coefficients of the symmetric group, which can be defined using Schur functions. In statistical mechanics, the partition functions of some integrable lattice models like lozenge tilings are often Lie group characters, and their asymptotic study reveals probabilistic behavior like Gaussian unitary ensemble eigenvalue distribution near the boundary or the existence of limit shapes and surfaces. This project aims to expand these applications to study other models and distributions. Studying combinatorial and algebraic properties of Schubert polynomials, as representatives of the cohomology classes of flag varieties, can lead to combinatorial interpretations for the corresponding structure constants. Further, computational properties of their stable versions, the Stanley symmetric functions, could lead to understanding of the mysterious limit behavior of random sorting networks, corresponding to the reduced decompositions of permutations into adjacent transpositions.", "AwardID" -> "1500834", "Institution" -> Entity["NSFInstitution", "UniversityOfPennsylvania"], "Investigators" -> {Entity["NSFInvestigator", "GretaPanova"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500834&HistoricalAwards=false"], "KeywordTally" -> {{"functions", 5}, {"symmetric", 4}, {"combinatorics", 3}, {"like", 3}, {"problems", 3}, {"project", 3}, {"structure", 3}, {"theory", 3}, {"algebraic", 2}, {"behavior", 2}, {"combinatorial", 2}, {"constants", 2}, {"corresponding", 2}, {"group", 2}, {"lattice", 2}, {"lead", 2}, {"limit", 2}, {"models", 2}, {"permutations", 2}, {"properties", 2}, {"sciences", 2}, {"study", 2}, {"symmetries", 2}, {"via", 2}}|>, "1500835" -> <|"AwardTitle" -> "Operator Theory Arising from Systems Engineering", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[218137, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Optimization is one of the areas most critical to modern technology, since designers always try to minimize cost or maximize performance, safety, output, etc. It can be thought of in two parts: convex optimization and nonconvex optimization. The concept of a convex function is illustrated by a cup; it has unique lowest point (minimum), while for nonconvex problems one would think of a mountain range with many valleys, hence many lowest points (local minima). Computer algorithms are good at finding one (or even a few) of local minima, but a major open problem is this: out of all the local minima, find the lowest (global) one. For convex problems all local minima are global, which means that computer runs do not report a false minimum. Of course, in technology the number of variables is huge, so all that is available to the designer are algebraic formulas (not pictures); thus the cup and mountain metaphors are misleadingly simple. There are two major classes of convex optimization problems solvable on a computer: classical linear programing and (within the last twenty years) the more widely applicable linear matrix inequalities (LMIs). This project concerns many aspects of LMIs, including the scope of LMI techniques: problems treatable with LMIs are convex, but conversely, which convex problems are treatable with LMIs? With collaborators the PI has sketched out a roadmap for this problem and pursues its confirmation. What one sees in linear systems engineering and control are problems with matrix unknowns. Simplifying physical problems and converting them to convex ones is currently done by ad hoc algebraic tricks. A major goal in this project is to develop a theory that will help systematize this. A particular concern is changes of variables to convert nonconvex problems to LMIs. Another is approximating a set with a convex set. In addition, the PI's group is the main provider to the public of software (called NCAlgebra) for performing general noncommuting algebra calculations in Mathematica. NCAlgebra is developed in the course of doing experiments for the proposed research.\n\nClassical real algebraic geometry develops a theory of (commutative) polynomials and much of it concerns inequalities based on evaluating them on tuples of real numbers. A good part of this project concerns noncommutative polynomials and their properties when evaluated on tuples of matrices (of all sizes). This new (freely) noncommutative real algebraic geometry often behaves much more rigidly than classical real algebraic geometry. While seeing how classical structure transports to free real algebraic geometry is part of the pursuit, engineering motivation and the highly rigid structure opens up new classes of problems. For example, free convexity, change of variables to achieve free convexity, free convex hulls, and free dilation theory are mathematically rich areas involving mixtures of functional analysis, optimization theory, algebra, and several complex variables. Also studied in this project are interactions with other subjects such as free probability as well as commutative topics related mostly to so-called linear matrix inequalities.", "AwardID" -> "1500835", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-SanDiego"], "Investigators" -> {Entity["NSFInvestigator", "JWilliamHelton"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500835&HistoricalAwards=false"], "KeywordTally" -> {{"convex", 9}, {"problems", 9}, {"algebraic", 6}, {"free", 6}, {"LMIs", 5}, {"real", 5}, {"geometry", 4}, {"linear", 4}, {"local", 4}, {"minima", 4}, {"optimization", 4}, {"project", 4}, {"theory", 4}, {"variables", 4}, {"classical", 3}, {"concerns", 3}, {"inequalities", 3}, {"lowest", 3}, {"major", 3}, {"matrix", 3}, {"nonconvex", 3}, {"algebra", 2}, {"areas", 2}, {"classes", 2}, {"commutative", 2}, {"computer", 2}, {"convexity", 2}, {"course", 2}, {"cup", 2}, {"engineering", 2}, {"global", 2}, {"good", 2}, {"minimum", 2}, {"mountain", 2}, {"NCAlgebra", 2}, {"new", 2}, {"noncommutative", 2}, {"polynomials", 2}, {"problem", 2}, {"set", 2}, {"structure", 2}, {"technology", 2}, {"treatable", 2}, {"tuples", 2}}|>, "1500837" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Between a tree and a dry place - How competition and drought tolerance constrain tree geographic ranges", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 5, 31}], "AwardAmount" -> Quantity[16297, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010208", "ProgramOfficer" -> "George Malanson", "Abstract" -> "Identifying the main constraints on species ranges and how these constraints vary across the globe has proven remarkably difficult; the degree to which the environment alone or in combination with interactions with other organisms imposes the limit is the crux of the problem. This project will combine experiments, field studies, and species distribution models to test whether plant species along a gradient from dry to wetter environments are squeezed between death from drought on one side of their range and fierce competition with species adapted to wetter conditions on the other. The results can help explain when, where, and how tree range boundaries are constrained, thereby advancing the state of the science. Such information may help guide land managers who seek to prepare for a rapidly changing climatic future by suggesting which conservation and forecasting tools are relevant in what situations, and thus enhances national welfare. It will also improve science education through activities for high school students.\n\nIt has long been hypothesized that plants are constrained by a fundamental trade-off between competitive ability and environmental stress tolerance, because adaptations to tolerate stress are energetically costly and limit maximum growth rates. Using seedling experiments, dendrochronological techniques, and species distribution modeling, this project explores whether tree species inhabiting aridity gradients in the U.S. and Australia show a trade-off between fast growth (a proxy for competitive ability) and drought tolerance. It then tests whether this trade-off mirrors growth constraints on adult trees in the field, and whether the observed trade-off and/or systematic growth constraints explain species turnover across aridity gradients. For broader impacts a module based on this research will be developed and piloted in cooperation with high school teachers, and results will be communicated to the public through a university teaching greenhouse.", "AwardID" -> "1500837", "Institution" -> Entity["NSFInstitution", "UniversityOfWashington"], "Investigators" -> {Entity["NSFInvestigator", "LeanderLove-Anderegg"], Entity["NSFInvestigator", "JannekeHilleRisLambers"]}, "ProgramElements" -> {{"Code" -> "1182", "Text" -> "POP & COMMUNITY ECOL PROG"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500837&HistoricalAwards=false"], "KeywordTally" -> {{"species", 7}, {"constraints", 4}, {"growth", 4}, {"trade-", 4}, {"ability", 2}, {"aridity", 2}, {"competitive", 2}, {"constrained", 2}, {"distribution", 2}, {"drought", 2}, {"experiments", 2}, {"explain", 2}, {"field", 2}, {"gradients", 2}, {"help", 2}, {"high", 2}, {"limit", 2}, {"project", 2}, {"range", 2}, {"results", 2}, {"school", 2}, {"science", 2}, {"stress", 2}, {"tolerance", 2}, {"tree", 2}, {"wetter", 2}}|>, "1500838" -> <|"AwardTitle" -> "Combinatorics, Representations, and Catalan Theory", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[180001, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This project studies problems at the interface of enumerative and algebraic combinatorics. Combinatorial questions arise in many areas of mathematics, and combinatorics has applications that include optimization, computer science, and statistical physics. The enumerative problems under study in this project are related to parking functions (which originally arose in the study of hash functions in computer science) and the cyclic sieving phenomenon (a concept in enumerative combinatorics that interprets certain polynomial evaluations as counts of fixed points). The research aims to both prove results in enumerative combinatorics and understand these results in terms of deeper algebraic structures. This interaction between combinatorics and algebra promises to yield new results in both fields. The enumerative side of the research is well-suited to broader impacts in the form of graduate and undergraduate research projects.\n\nThis project studies problems in algebraic combinatorics. The first of these is the cyclic sieving phenomenon as it applies to the action of a K-theoretic analog of the promotion operator on a K-generalization of rectangular standard Young tableaux. The idea is to prove new instances of the (enumerative) cyclic sieving phenomenon related to this action using representation theory. The second problem concerns a generalization of parking functions attached to the symmetric group to a wider class of \"parking spaces\" attached to a reflection group W. We study a family of conjectures regarding these objects which would yield uniform proofs of various facts in Coxeter-Catalan theory which are at present only understood in a case-by-case fashion. The third project studies rational Catalan combinatorics, which is a generalization of classical Catalan combinatorics motivated by the study of rational Cherednik algebras. We propose to both extend various results from the rich enumerative domain of the classical setting to the rational case and study a genuinely new feature of the rational case that we call \"rational duality.\"", "AwardID" -> "1500838", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-SanDiego"], "Investigators" -> {Entity["NSFInvestigator", "BrendonRhoades"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500838&HistoricalAwards=false"], "KeywordTally" -> {{"combinatorics", 8}, {"enumerative", 7}, {"rational", 5}, {"study", 5}, {"project", 4}, {"results", 4}, {"algebraic", 3}, {"cyclic", 3}, {"functions", 3}, {"new", 3}, {"parking", 3}, {"phenomenon", 3}, {"problems", 3}, {"research", 3}, {"sieving", 3}, {"studies", 3}, {"action", 2}, {"attached", 2}, {"case", 2}, {"Catalan", 2}, {"classical", 2}, {"computer", 2}, {"generalization", 2}, {"group", 2}, {"prove", 2}, {"related", 2}, {"science", 2}, {"theory", 2}, {"various", 2}, {"yield", 2}}|>, "1500841" -> <|"AwardTitle" -> "CoLang 2016: Institute on Collaborative Language Research - ALASKA", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2017, 7, 31}], "AwardAmount" -> Quantity[158000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "The 2016 Institute on Collaborative Language Research (CoLang 2016) will be held at the University of Alaska Fairbanks. CoLang brings together leading practitioners of language documentation from across the world to provide cutting-edge training in language documentation techniques and collaborative practices. Over a period of five weeks, including two weeks of workshops followed by three-week, in-depth field methods classes, participants engage in hands-on training in best practices in linguistic field research. Uniquely, CoLang focuses on collaborative documentation, engaging specialists from within language communities of underrepresented groups with academicians in knowledge sharing. All participants learn and teach, providing formal instruction via workshops or practicum teaching, participating in classes that take them out of their familiar areas and challenge them to engage with cultures and material new to them, and by networking with their colleagues around the world. In this way, CoLang builds a growing network of language workers who support each other in developing valid and sustainable approaches to language documentation.", "AwardID" -> "1500841", "Institution" -> Entity["NSFInstitution", "UniversityOfAlaskaFairbanksCampus"], "Investigators" -> {Entity["NSFInvestigator", "LawrenceKaplan"], Entity["NSFInvestigator", "SiriTuttle"], Entity["NSFInvestigator", "AliceTaff"]}, "ProgramElements" -> {{"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "1744", "Text" -> "TRIBAL COLLEGE & UNIVERS PROGR"}}, "ProgramReferences" -> {{"Code" -> "1311", "Text" -> "LINGUISTICS"}, {"Code" -> "5221", "Text" -> "ARCTIC SOCIAL SCIENCES"}, {"Code" -> Missing["NotAvailable"], "Text" -> Missing["NotAvailable"]}, {"Code" -> "8050", "Text" -> "Science of Broadening Participation"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500841&HistoricalAwards=false"], "KeywordTally" -> {{"language", 5}, {"CoLang", 4}, {"documentation", 4}, {"2016", 2}, {"classes", 2}, {"collaborative", 2}, {"engage", 2}, {"field", 2}, {"participants", 2}, {"practices", 2}, {"training", 2}, {"weeks", 2}, {"workshops", 2}, {"world", 2}}|>, "1500848" -> <|"AwardTitle" -> "SHF: Medium: ASKS - Architecture Support for darK Silicon", "AwardEffectiveDate" -> DateObject[{2014, 8, 16}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[920428, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "05010000", "ProgramOfficer" -> "Tao Li", "Abstract" -> "The proposed ASKS (Architecture Support for darK Silicon) project proposes architectural support for future many-core microprocessors designed with and around emerging technologies to address the challenges of the coming dark silicon revolution. Future many-cores, to stay on the historical performance curve, will contain more transistors than can all be sustainably powered at the same time. Thus, we face the prospect of ?dark silicon,? wherein some of a chip?s components must be powered-off (darkened) in order to stay within the chip?s power/thermal budget. Ensuring peak performance under these circumstances is a challenging task. In particular, in an architecture with different types of components (cores, caches, network on chip (NoC, or on-chip interconnet), memory controllers, etc.), there can be many different on-dim-dark configurations within the power budget. However, these can exhibit significantly varying performances. Additionally, the power consumption of uncore components (shared caches, on-chip interconnect, memory architecture) is significant, thus the uncore components play an important role in joint performance/power/thermal optimization. Therefore, a more inclusive approach is needed. Our architectural design space exploration will mainly focus on the uncore space (shared caches, on-chip interconnect structures, memory architecture), targeting future NoC-based many-core microprocessors that exploit the emerging technologies of 3D die-stacking (3D IC) and non-volatile memories (NVM).\n\nThis project will advance the state of the art in preparing for the dark silicon revolution in two main aspects. 1) Cross-layer holistic optimization with a focus on uncore components: The uncore components play important roles in joint performance/power/thermal optimization. This project proposes an integrated approach in which the cores and uncore components collaborate to maximize performance under power and thermal constraints as well as under dynamically changing program behavior and execution parameters. 2) Investigating dark silicon in the context of emerging technologies: Emerging 3D ICs and NVM technologies are envisioned as promising ways to design future many-core architectures. The adoption of such emerging technologies poses new challenges for dark silicon (such as aggravated thermal profiles in 3D stacked chips), but also brings new opportunities for architectural innovations such as novel power management techniques and greater exploitation of memory system heterogeneity. The broader impact of this project includes the contribution to the increased performance for future microprocessors even in the face of the coming dark silicon revolution. Through close collaboration with several industry partners, the PIs envision direct transfer of many ideas to industry. The tools and techniques developed in this project will be used in teaching existing courses and developing new courses, and will be made available through the web for use by other educators, researchers, and industry practitioners. Dissemination of research findings will also be carried out through conference tutorials, panel discussions, and workshops. A concerted effort will be made to involve under-represented groups and undergraduate students in this research.", "AwardID" -> "1500848", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-SantaBarbara"], "Investigators" -> {Entity["NSFInvestigator", "YuanXie"]}, "Directorate" -> "Direct For Computer & Info Scie & Enginr", "Division" -> "Division of Computing and Communication Foundations", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500848&HistoricalAwards=false"], "KeywordTally" -> {{"components", 7}, {"dark", 6}, {"silicon", 6}, {"uncore", 6}, {"power", 5}, {"project", 5}, {"technologies", 5}, {"3D", 4}, {"emerging", 4}, {"future", 4}, {"memory", 4}, {"performance", 4}, {"architectural", 3}, {"architecture", 3}, {"caches", 3}, {"-chip", 3}, {"chip", 3}, {"-core", 3}, {"industry", 3}, {"microprocessors", 3}, {"new", 3}, {"optimization", 3}, {"revolution", 3}, {"thermal", 3}, {"approach", 2}, {"budget", 2}, {"challenges", 2}, {"coming", 2}, {"cores", 2}, {"courses", 2}, {"design", 2}, {"different", 2}, {"face", 2}, {"focus", 2}, {"important", 2}, {"interconnect", 2}, {"joint", 2}, {"performance/power/thermal", 2}, {"play", 2}, {"proposes", 2}, {"research", 2}, {"s", 2}, {"shared", 2}, {"space", 2}, {"stay", 2}, {"techniques", 2}}|>, "1500850" -> <|"AwardTitle" -> "Conformal invariance and the renormalization group in some critical systems", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[239310, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "Many models in physics are inherently discrete at the very smallest scale (typically the size of an atom) and there is inherent randomness at this discrete level. At the macroscopic level the randomness is typically not seen. But under certain conditions this randomness manifests itself at the macroscopic scale. This is known as a critical phenomena. For example, the spins in a magnetic material have randomness in their orientation. At a certain temperature these spins can align with each other to produce macroscopic magnetic domains that play a crucial role in technological applications such as hard drives. The randomness seen at the macroscopic scale often does not depend on the details of the microscopic randomness. In physics this is called universality and has developed into a key idea in the understanding of critical phenomena. The renormalization group is set of methods from physics that has become the basis for the modern understanding of both critical phenomena and of quantum field theory - the theory of elementary particles. Despite the tremendous success of the renormalization group in physics, we do not have a deep mathematical understanding of this set of ideas. This research will further the mathematical development and understanding of this set of ideas and methods and use them to understand the mathematics of critical phenomena in models such as self-avoiding random walks and Ising models of magnetic spins.\n\nMost of the research will be devoted to random walk models and Ising-type models. The smart kinetic walk (also known as a limiting case of the Laplacian-b random walk) is a dynamic model for self-avoiding walks. On the hexagonal lattice it is closely related to percolation. Percolation methods have been used to prove its scaling limit is the Schramm-Loewner evolution with parameter value 6. The research will study this scaling limit on other lattices and for generalizations of the transition probabilities. The goal is to understand the universality of this scaling limit. For the ordinary random walk the scaling limit of the exit distribution for a domain is harmonic measure. Another goal of the research is to understand the first order correction for this convergence for both the ordinary random walk and the smart kinetic walk. The research will also study real space renormalization groups for Ising type models, in particular exact renormalization group transformations in one and two dimensions. These transformation have the potential advantage that the map would act on a finite dimensional space. The goal is to prove that the map can be rigorously defined and then take advantage of the finite dimensional nature to prove existence of a fixed point and all the exciting consequences that follow from this existence. Finally the research will study Schramm-Loewner evolution as a renormalization group fixed point. This stochastic process is known to be the scaling limit of many critical models. The goal here is to define a renormalization group map that has this process as a fixed point and then use this map to understand models that are near criticality.", "AwardID" -> "1500850", "Institution" -> Entity["NSFInstitution", "UniversityOfArizona"], "Investigators" -> {Entity["NSFInvestigator", "ThomasKennedy"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500850&HistoricalAwards=false"], "KeywordTally" -> {{"models", 8}, {"randomness", 6}, {"renormalization", 6}, {"research", 6}, {"walk", 6}, {"critical", 5}, {"group", 5}, {"limit", 5}, {"random", 5}, {"scaling", 5}, {"goal", 4}, {"macroscopic", 4}, {"map", 4}, {"phenomena", 4}, {"physics", 4}, {"understand", 4}, {"understanding", 4}, {"fixed", 3}, {"known", 3}, {"magnetic", 3}, {"methods", 3}, {"point", 3}, {"prove", 3}, {"scale", 3}, {"set", 3}, {"study", 3}, {"advantage", 2}, {"certain", 2}, {"dimensional", 2}, {"discrete", 2}, {"evolution", 2}, {"existence", 2}, {"finite", 2}, {"ideas", 2}, {"Ising", 2}, {"kinetic", 2}, {"level", 2}, {"mathematical", 2}, {"ordinary", 2}, {"process", 2}, {"Schramm-Loewner", 2}, {"seen", 2}, {"self-avoiding", 2}, {"smart", 2}, {"space", 2}, {"spins", 2}, {"theory", 2}, {"typically", 2}, {"universality", 2}, {"use", 2}, {"walks", 2}}|>, "1500851" -> <|"AwardTitle" -> "Understanding Evidentiality and other grammatical phenomena through the expanded Documentation of Hupa", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[245018, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "04040000", "ProgramOfficer" -> "Colleen Fitzgerald", "Abstract" -> "Hupa, a critically endangered Native American language of northwestern California, has a rich system of grammatical markers called evidentials that speakers deploy to indicate sources of information and viewpoint in narratives. Details of the distinctive Hupa system are still largely unexplored but have tremendous potential to improve our general understanding of how such meanings are expressed in human languages. \n\nIn this three-year Documenting Endangered Languages project, Justin Spence of the University of California, Davis and Ramon Excamilla of the University of Central Arkansas will work with Hupa elder Verdena Parker to obtain narrative interpretations of archival film footage and translations of yet unanalyzed recordings. In conjunction with targeted elicitations, analysis of the resulting Hupa language samples will help develop typologically and theoretically situated descriptions of evidentiality and other aspects of Hupa discourse structure. \n\nPublic access to material produced by the project will be achieved through improvements to an existing online dictionary and text database. Expanding the quantity of accessible transcribed texts and the coverage of the dictionary, together with improvements to the user interface, will allow users to perform more sophisticated queries and to have greater confidence in the accuracy of the results they obtain. \n\nAll recordings and transcriptions produced by the project will be archived with the Survey of California and Other Indian Languages at UC Berkeley, ensuring that they will remain accessible to future generations of users for many years to come.", "AwardID" -> "1500851", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Davis"], "Investigators" -> {Entity["NSFInvestigator", "RamonEscamilla"], Entity["NSFInvestigator", "JustinSpence"]}, "Directorate" -> "Direct For Social, Behav & Economic Scie", "Division" -> "Division Of Behavioral and Cognitive Sci", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500851&HistoricalAwards=false"], "KeywordTally" -> {{"Hupa", 5}, {"California", 3}, {"project", 3}, {"accessible", 2}, {"br/>

", 2}, {"dictionary", 2}, {"improvements", 2}, {"language", 2}, {"Languages", 2}, {"obtain", 2}, {"produced", 2}, {"recordings", 2}, {"system", 2}, {"University", 2}, {"users", 2}}|>, "1500852" -> <|"AwardTitle" -> "Semiclassical Analysis", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2020, 6, 30}], "AwardAmount" -> Quantity[125000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "The PI studies mathematical problems motivated by quantum mechanics, wave propagation, and chaotic dynamics, in particular, oscillations and decay of waves. Just as a bell sounds a fading note, a wave or an unstable molecule oscillates and decays at certain rates. These two rates (of oscillation and of decay) are properties of the system and not of the way in which it is measured. Understanding their behaviour can be useful both in construction and in detection. For instance, in engineering, the ratio of the two rates is called the quality factor and tells us the amount of energy loss per cycle. Knowing this ratio for modes of specific systems is important in design of, for instance, microelectromechanical systems (MEMS). On a different scale, similar modes appear in gravitational waves generated by colliding black holes and their (hypothetical) detection could provide information about black holes. The PI searches for unifying themes connecting the distribution of these modes and geometries of various systems.\n\nMany physical systems can be described using evolution of states. The following correlations are observed: one measures the time evolution of one state against another state. The time representation can be replaced by the frequency representation (by taking a Fourier transform) which produces the power spectrum. The poles of power spectrum appear in different settings and are called scattering poles (obstacle scattering), quantum resonances (quantum scattering theory), quasinormal modes (general relativity), Pollicott--Ruelle resonances (chaos theory). These poles provide information about long time behaviour: the real part corresponds to the rate of oscillations, and the imaginary part to the rate of decay. The PI studies these poles in the different settings mentioned above. One recurrent theme is the use of the classical/quantum (wave) correspondence which suggests subtle interplay between \"classical\" properties of the system and properties of waves. The PI investigates this phenomenon in many settings, in particular when chaotic behaviour is present on the classical level. Most recently methods that were developed for the study of classical quantum correspondence (microlocal analysis) became useful in the study of purely dynamical problems such as meromorphic continuations of zeta functions and problems in X-ray tomography.", "AwardID" -> "1500852", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Berkeley"], "Investigators" -> {Entity["NSFInvestigator", "MaciejZworski"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500852&HistoricalAwards=false"], "KeywordTally" -> {{"quantum", 5}, {"classical", 4}, {"modes", 4}, {"PI", 4}, {"poles", 4}, {"behaviour", 3}, {"decay", 3}, {"different", 3}, {"problems", 3}, {"properties", 3}, {"rates", 3}, {"scattering", 3}, {"settings", 3}, {"systems", 3}, {"time", 3}, {"wave", 3}, {"waves", 3}, {"appear", 2}, {"black", 2}, {"called", 2}, {"chaotic", 2}, {"correspondence", 2}, {"detection", 2}, {"evolution", 2}, {"holes", 2}, {"information", 2}, {"instance", 2}, {"oscillations", 2}, {"particular", 2}, {"power", 2}, {"provide", 2}, {"rate", 2}, {"ratio", 2}, {"representation", 2}, {"resonances", 2}, {"spectrum", 2}, {"state", 2}, {"studies", 2}, {"study", 2}, {"system", 2}, {"theory", 2}, {"useful", 2}}|>, "1500856" -> <|"AwardTitle" -> "RUI: Extremal Combinatorics of Patterns, Correlation, and Structure", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[150000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "Combinatorics considers finite structures, many of which play a crucial role in problems that arise in science and technology. Preeminent among these structures are finite binary sequences (strings of zeroes and ones) that are used in the communications networks, cryptographic systems, remote sensing, acoustic design, and efficient operation of scientific instrumentation. Other finite structures arising from polynomials, sets, and graphs also find use in a wide variety of technological and scientific endeavors. To achieve an engineering goal or understand a natural process, one must often find the structures that are extremal (minimal or maximal) with respect to a certain feature. For example, we might seek a family of binary sequences that resemble each other as little as possible in order avoid mutual interference in a multi-user communications network: this is the problem of low correlation. The solutions to such extremal problems often involve mathematical objects with a large amount of structure. This research project aims to investigate some problems in extremal combinatorics and the mathematical structures involved in these extremal problems.\n\nThe organizing principle of this project is to investigate important problems in pure mathematics involving highly structured discrete objects, many of which are of great interest in science and technology. For example, the problem of minimizing aperiodic autocorrelation of binary sequences is of vital importance in engineering applications like remote sensing and communication. Later, physicists noted that the minima describe the ground states of certain systems in statistical physics. Yet the problem is also related to questions in harmonic analysis raised by Littlewood in 1966 and still actively researched, with recent contributions from the principal investigator that are being further developed. Problems such as this are rich in connections to other branches of mathematics, because the optimal or best known discrete structures for them often come from fields like number theory, algebra, or geometry. For example, the sequences with lowest known asymptotic aperiodic autocorrelation derive from the Fekete polynomials in analytic number theory. The Weil sums studied in this project originate in number theory and arithmetic algebraic geometry: they provide a method for counting points on curves over finite fields. In technology, they determine the nonlinearity of functions used in cryptography, the weight distribution of error-correcting codes, and the cross-correlation properties of linear recursive sequences over finite fields. New techniques to bound the maximum number of instances of a pattern in a finite set of points in the plane utilize diverse techniques that range from order relations to topological arguments. The interplay of all these ideas, pure and applied, leads to a mutual enrichment of mathematics, engineering, and science.", "AwardID" -> "1500856", "Institution" -> Entity["NSFInstitution", "TheUniversityCorporation,Northridge"], "Investigators" -> {Entity["NSFInvestigator", "DanielKatz"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500856&HistoricalAwards=false"], "KeywordTally" -> {{"finite", 6}, {"structures", 6}, {"sequences", 5}, {"extremal", 4}, {"number", 4}, {"problems", 4}, {"binary", 3}, {"engineering", 3}, {"example", 3}, {"fields", 3}, {"mathematics", 3}, {"problem", 3}, {"project", 3}, {"science", 3}, {"technology", 3}, {"theory", 3}, {"aperiodic", 2}, {"autocorrelation", 2}, {"certain", 2}, {"communications", 2}, {"discrete", 2}, {"geometry", 2}, {"investigate", 2}, {"known", 2}, {"like", 2}, {"mathematical", 2}, {"mutual", 2}, {"objects", 2}, {"order", 2}, {"points", 2}, {"polynomials", 2}, {"pure", 2}, {"remote", 2}, {"scientific", 2}, {"sensing", 2}, {"systems", 2}, {"techniques", 2}, {"used", 2}}|>, "1500868" -> <|"AwardTitle" -> "p-adic Methods in Number Theory", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2017, 4, 30}], "AwardAmount" -> Quantity[40000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "This award provides support for participation in the conference \"p-adic Methods in Number Theory\" held at the University of California, Berkeley on May 26-30, 2015. Since their conception by Kurt Hensel around 1900, p-adic numbers have played a central role in number theory; for example, they are used in a crucial way in the proof of Fermat's Last Theorem. To a number theorist, p-adic numbers are just as \"real\" -- and just as important -- as real numbers. Both are ways of \"filling in the gaps\" left by considering just rational numbers. In their book \"Number Theory I: Fermat's Dream,\" Kato, Kurokawa, and Saito write poetically, \"In the long history of mathematics a number meant a real number, and it is only relatively recently that we realized that there is a world of p-adic numbers. It is as if those who had seen the sky only during the day are marveling at the night sky. [ ] Just as we can see space objects better at night, we begin to see the profound mathematical universe through the p-adic numbers.\" This conference will bring together experts in the many different facets of p-adic numbers and their applications, will promote a cross-fertilization of ideas between number theorists of all stripes, will expose graduate students and postdocs to state-of-the-art techniques and results, and will promote participation by underrepresented minorities and women in high-level number theory research. \n\nA conference on p-adic methods in number theory is timely and important, as many spectacular recent number-theoretic advances have made use of deep p-adic methods. We mention, for example, recent work establishing special cases of the p-adic local Langlands correspondence; the proof that most hyperelliptic curves of odd degree have just one rational point; developments on non-abelian Coleman integration and integral points on curves; work on the fundamental curve of p-adic Hodge theory; and recent results on perfectoid spaces. More Information can be found at https://sites.google.com/site/padicmethods2015/.", "AwardID" -> "1500868", "Institution" -> Entity["NSFInstitution", "GeorgiaTechResearchCorporation"], "Investigators" -> {Entity["NSFInvestigator", "MatthewBaker"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500868&HistoricalAwards=false"], "KeywordTally" -> {{"p-adic", 10}, {"number", 7}, {"numbers", 7}, {"just", 4}, {"theory", 4}, {"conference", 3}, {"real", 3}, {"recent", 3}, {"curves", 2}, {"example", 2}, {"Fermat's", 2}, {"important", 2}, {"methods", 2}, {"night", 2}, {"Number", 2}, {"participation", 2}, {"promote", 2}, {"proof", 2}, {"rational", 2}, {"results", 2}, {"sky", 2}, {"Theory", 2}, {"work", 2}}|>, "1500871" -> <|"AwardTitle" -> "Analytical and geometrical properties of non linear diffusion equations", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2020, 5, 31}], "AwardAmount" -> Quantity[228270, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "This research project is focused mainly on aspects of diffusion processes. The mathematical idea of diffusion is an attempt to quantify and model how a species, a fluid, heat, particles, or information spreads out in time due to the effect of pressure (as in particles or populations) or by other neighbor-to-neighbor interaction, as in the case of information dynamics. One of the ways in which diffusion has been described mathematically is through partial differential equations, which model infinitesimal adjacent interactions. With mathematical modeling in fields like biology, finance, and the social sciences, the need has emerged of understanding phenomena where the diffusion process takes into consideration long-range information or interactions; that is the case when particles are transported, information is communicated simultaneously at many scales, organisms communicate by the creation of a chemical potential, or stocks change value in discontinuous ways. The PI will study diverse phenomena related to these processes with long interactions in space and time (memory), such as flows in reservoirs that clog with time, segregation processes that occur at a distance, or models in price formation where there is a gap between buyers and sellers.\n\nA first area of research encompasses nonlinear problems involving nonlocality in both space and time. From the stochastic side, the model is the continuous in time random walk equation, which involves Levy walks instead of jumps. From the variational side, there are diverse models for porous medium flows with potential pressures, where the medium is deformed by the flow. These involve study of fully nonlinear equations of nonlocal type that by the nature of their invariant properties parallel equations involving symmetric functions of the Hessian, such as the Monge-Ampere equation. Another area of investigation involves phase transitions and free boundary problems. One group concerns models for segregation of species, optimal partition of a domain by disjoint subdomains optimizing some \"shape\" value function. Another group deals with the homogenization of fronts in random or periodic media, and a third concerns the regularity of free boundaries for some stationary or evolution problems. The issues described above are universal in the sense that the same paradigm reappears in geometry and analysis, fluid dynamics and material sciences, financial mathematics, and more recently biology and stochastic geometry.", "AwardID" -> "1500871", "Institution" -> Entity["NSFInstitution", "UniversityOfTexasAtAustin"], "Investigators" -> {Entity["NSFInvestigator", "LuisCaffarelli"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500871&HistoricalAwards=false"], "KeywordTally" -> {{"time", 5}, {"diffusion", 4}, {"information", 4}, {"equations", 3}, {"interactions", 3}, {"model", 3}, {"models", 3}, {"particles", 3}, {"problems", 3}, {"processes", 3}, {"area", 2}, {"biology", 2}, {"case", 2}, {"concerns", 2}, {"described", 2}, {"diverse", 2}, {"dynamics", 2}, {"equation", 2}, {"flows", 2}, {"fluid", 2}, {"free", 2}, {"geometry", 2}, {"group", 2}, {"involves", 2}, {"involving", 2}, {"mathematical", 2}, {"medium", 2}, {"nonlinear", 2}, {"phenomena", 2}, {"potential", 2}, {"random", 2}, {"research", 2}, {"sciences", 2}, {"segregation", 2}, {"space", 2}, {"species", 2}, {"stochastic", 2}, {"study", 2}, {"value", 2}, {"ways", 2}}|>, "1500875" -> <|"AwardTitle" -> "Moduli Spaces of Holomorphic Curves: Properties and Applications", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[214000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "String theory is a model that represents elementary particles by vibrating strings with the aim of unifying the four fundamental forces of nature. While string theory is one of the main paradigms in physics today, it has yet to make experimentally testable predictions. However, it has generated many mathematical predictions that have led to fundamental developments in algebraic geometry and symplectic topology, especially in relation to (pseudo-) holomorphic curves. This project aims to further test string theory mathematically, while deepening the mathematical understanding of such curves with an eye toward applications to more classical problems in geometry. Some of the projects in this work will be pursued by graduate students and other junior researchers in collaboration with the investigator.\n\nThis project has four distinct directions at the juncture of algebraic geometry, symplectic topology, and string theory. It will explore connections between the rigidity of pseudo-holomorphic curves in symplectic topology and birational algebraic geometry. It will study the local structure of moduli spaces of stable morphisms of genus 2 and higher, with the aim of later applications in mirror symmetry and enumerative geometry. The PI will also apply his method for computing genus 1 Gromov-Witten invariants to more targets, with the aims of verifying predictions of string theory predictions in additional cases. The fourth direction aims to develop positive-genus real Gromov-Witten theory and its relations with open string theory and real enumerative geometry.\n\nThis award is jointly funded by the Algebra and Number Theory and Geometric Analysis programs.", "AwardID" -> "1500875", "Institution" -> Entity["NSFInstitution", "SUNYAtStonyBrook"], "Investigators" -> {Entity["NSFInvestigator", "AlekseyZinger"]}, "ProgramElements" -> {{"Code" -> "1265", "Text" -> "GEOMETRIC ANALYSIS"}, {"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500875&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 7}, {"geometry", 5}, {"string", 5}, {"predictions", 4}, {"aims", 3}, {"algebraic", 3}, {"curves", 3}, {"symplectic", 3}, {"topology", 3}, {"aim", 2}, {"applications", 2}, {"enumerative", 2}, {"fundamental", 2}, {"genus", 2}, {"Gromov-Witten", 2}, {"mathematical", 2}, {"project", 2}, {"real", 2}}|>, "1500881" -> <|"AwardTitle" -> "The Geometry of Measures and Regularity of Associated Operators", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[38941, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This project concerns a study of the some of the mathematics behind the following basic physical question: To what extent can the geometry of a body be determined from information about a force field associated to the body (for instance, its gravitational field)? Such inverse problems in potential theory have a rich history, but the mathematical tools needed to properly answer this question, especially in the case when the operator relating the force field to the mass distribution of the body is sensitive to long-range interactions, are currently underdeveloped. In this project, the principal investigator will develop tools to further understand this problem, concentrating especially on what can be said if one knows only that the field has bounded magnitude.\n\nMore specifically, the project primarily concerns the relationship between the geometry of a measure and the regularity of an associated differential or singular integral operator. This is is a question that has attracted mathematicians ever since the Cauchy and Riesz transforms were introduced as tools to study the behavior of analytic and harmonic functions, respectively. An integrated approach to such problems is proposed that goes through the study of reflectionless measures. This approach has recently yielded several new results and could potentially address a number of open problems, especially those concerning the smoothness of the support of a measure that has a bounded Riesz transform. Here new tools in quantitative geometry and higher order partial differential equations need to be developed in order to make progress. Furthermore, the principal investigator seeks to build upon recent innovations in the theory of quasilinear differential equations to consider analogous problems for a wide range of nonlinear differential operators, where no integral representation is available.", "AwardID" -> "1500881", "Institution" -> Entity["NSFInstitution", "KentStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "BenjaminJaye"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500881&HistoricalAwards=false"], "KeywordTally" -> {{"differential", 4}, {"field", 4}, {"problems", 4}, {"tools", 4}, {"body", 3}, {"especially", 3}, {"geometry", 3}, {"project", 3}, {"question", 3}, {"study", 3}, {"approach", 2}, {"associated", 2}, {"bounded", 2}, {"concerns", 2}, {"equations", 2}, {"force", 2}, {"integral", 2}, {"investigator", 2}, {"measure", 2}, {"new", 2}, {"operator", 2}, {"order", 2}, {"principal", 2}, {"Riesz", 2}, {"theory", 2}}|>, "1500890" -> <|"AwardTitle" -> "Modular Representation Theory and Geometric Langlands Duality", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[191790, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Matthew Douglass", "Abstract" -> "A matrix group is a set of invertible square matrices that contains all products and inverses of its members. Representation theory is a branch of algebra concerned with studying symmetries, especially symmetries arising from matrix groups. Modular representation theory is the branch of representation theory concerned with matrix groups whose entries come from a finite field. It has deep connections with number theory, combinatorics, and geometry. This research project aims to make advances in modular representation theory using geometric methods.\n\nThis research project aims to make advances in the representation theory of algebraic groups over a field of positive characteristic via the philosophy of local geometric Langlands duality. Specifically, the PI hopes to establish a collection of derived equivalences in positive characteristic modeled on characteristic zero results. This work will lead to explicit connections between between the following notions: (i) modular representations of algebraic groups; (ii) modular perverse sheaves and parity sheaves on the affine Grassmannian and the affine flag variety; and (iii) the phenomena of Koszul and Q-Koszul duality.", "AwardID" -> "1500890", "Institution" -> Entity["NSFInstitution", "LouisianaStateUniversity&AgriculturalAndMechanicalCollege"], "Investigators" -> {Entity["NSFInvestigator", "PramodAchar"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500890&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 6}, {"groups", 4}, {"representation", 4}, {"characteristic", 3}, {"matrix", 3}, {"modular", 3}, {"advances", 2}, {"affine", 2}, {"aims", 2}, {"algebraic", 2}, {"branch", 2}, {"concerned", 2}, {"connections", 2}, {"duality", 2}, {"field", 2}, {"geometric", 2}, {"make", 2}, {"positive", 2}, {"project", 2}, {"research", 2}, {"sheaves", 2}, {"symmetries", 2}}|>, "1500893" -> <|"AwardTitle" -> "Asymptotic Analysis of Partial Differential Equations and Systems with Emphasis on Boundary Layers", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2015, 9, 30}], "AwardAmount" -> Quantity[29830, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This research proposal is devoted to the understanding of the effect of small scale heterogeneities on solutions of Partial Differential Equations (PDEs). Systems having structures at several spatial and temporal scales, micro-, meso- or macroscopic scales, are ubiquitous in industry (composite materials, microfluidics), in biology (tissues, cell membranes, brain), in geophysics (seabed), in meteorology (clouds), in fluid mechanics (turbulence) and in physics (granular materials, structure of matter). The general spirit of the mathematical study is to figure out how one can integrate these small scales into asymptotic simplified models. Moreover, this work focuses on the understanding of the interactions between the different scales from a dynamical point of view: memory effects, energy transfers, instabilities and out of equilibrium dynamics. This fundamental research has far reaching consequences. This work underlies the design of new numerical methods, aims at proving the accuracy of numerical schemes and enables to improve their efficiency. \n\nThis proposal focuses on the study of the boundary behavior of solutions and on the analysis of equations and systems with low regularity, either in the coefficients, or in the boundary. A lot of the existing theory of PDEs, even for elliptic problems, has been developed for equations, in smooth domains, with constant or smooth coefficients, with symmetry. Similarly, the derivation of asymptotic models often relies on strong structure assumptions such as periodicity. New applications have made the need for relaxing these assumptions even more important. These questions lead to many challenging open problems. The primary goals are to (i) develop the tools for non symmetric elliptic equations and systems with non constant coefficients, (ii) investigate highly oscillating boundary conditions, (iii) relax structure assumptions in problems concerned with oscillating boundaries, (iv) make progress in the analysis of stationary linear or nonlinear systems in infinite energy spaces motivated by the study of boundary layers, (v) provide tractable results for numerical homogenization and (vi) justify rigorously some asymptotic models in oceanography and in the theory of viscoelastic fluids. This area of research is currently very active, and the proposed problems are important. The PI and his collaborators have elaborated new methods in recent works to deal with such questions. Developing these tools further will not only help solve the problems (i)-(vi) but also bring new ideas to many fields of PDEs: homogenization, harmonic analysis, elliptic equations and systems, and fluid mechanics.", "AwardID" -> "1500893", "Institution" -> Entity["NSFInstitution", "UniversityOfChicago"], "Investigators" -> {Entity["NSFInvestigator", "ChristophePrange"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500893&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 5}, {"boundary", 4}, {"equations", 4}, {"scales", 4}, {"systems", 4}, {"analysis", 3}, {"assumptions", 3}, {"asymptotic", 3}, {"coefficients", 3}, {"elliptic", 3}, {"models", 3}, {"new", 3}, {"numerical", 3}, {"PDEs", 3}, {"research", 3}, {"structure", 3}, {"study", 3}, {"constant", 2}, {"energy", 2}, {"fluid", 2}, {"focuses", 2}, {"homogenization", 2}, {"important", 2}, {"materials", 2}, {"mechanics", 2}, {"methods", 2}, {"non", 2}, {"oscillating", 2}, {"proposal", 2}, {"questions", 2}, {"small", 2}, {"smooth", 2}, {"solutions", 2}, {"theory", 2}, {"tools", 2}, {"understanding", 2}, {"vi", 2}, {"work", 2}}|>, "1500897" -> <|"AwardTitle" -> "INSTABILITIES IN DYNAMICAL SYSTEMS", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[130000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "In this project instabilities in dynamical systems will be studied. In dynamical systems the way in which a system obeying some fixed rules evolves over time is studied. The long term behavior of a deterministic dynamical system may be chaotic and unpredictable. Such behavior is termed \"instability\". An example is the well-known butterfly effect, where there is a sensitive dependence on the initial conditions in which a small change of the initial state of a system may lead to huge differences in later states. The proposed research will study instabilities of systems arising in classical mechanics and general relativity. The goal is to understand how the instability occurs and to quantify its properties. Another goal is to discover unknown phenomena based on a new understanding of instability mechanisms.\n\nThe proposed projects fall into the following three different fields. The first project is to study Hamiltonian systems using symplectic methods. This will be a continuation of previous work. It includes finding periodic orbits and homoclinic or heteroclinic orbits satisfying certain topological constraints in non-convex Hamiltonian systems. The next project is to try to use the methods of proving Arnold diffusion to study systems in general relativity. The interest is in showing Arnold diffusion in a perturbed Kerr-de Sitter metric and the physical meaning of Arnold diffusion in this setting is the Penrose process for energy and angular momentum extraction from black hole. In the last project the PI and his collaborators will use a general dynamical system without Hamiltonian structure to produce positive Lyapunov exponents in concrete systems with the help of small random perturbations. In particular, for two dimensions the methods show positive Lyapunov exponents for a randomly perturbed standard map.", "AwardID" -> "1500897", "Institution" -> Entity["NSFInstitution", "UniversityOfChicago"], "Investigators" -> {Entity["NSFInvestigator", "JinxinXue"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500897&HistoricalAwards=false"], "KeywordTally" -> {{"systems", 7}, {"dynamical", 4}, {"project", 4}, {"system", 4}, {"Arnold", 3}, {"diffusion", 3}, {"general", 3}, {"Hamiltonian", 3}, {"instability", 3}, {"methods", 3}, {"study", 3}, {"behavior", 2}, {"exponents", 2}, {"goal", 2}, {"initial", 2}, {"instabilities", 2}, {"Lyapunov", 2}, {"orbits", 2}, {"perturbed", 2}, {"positive", 2}, {"proposed", 2}, {"relativity", 2}, {"small", 2}, {"studied", 2}, {"use", 2}}|>, "1500900" -> <|"AwardTitle" -> "Toward and Improved Understanding and Parameterization of the Stable Atomospheric Boundary Layer", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[128859, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "06020105", "ProgramOfficer" -> "Edward L. Bensman", "Abstract" -> "This study will use a database of very high-resolution model simulations of the lowest layers of the atmosphere to compare with known output from various models of the turbulent layer near the earth's surface. The goal of this research is to improve the way in which air flow is modeled in the very lowest layers of the atmosphere, near the ground. This study will add valuable insight into the success of various numerical prediction schemes and may ultimately lead to improvements in these schemes used in weather models. One undergraduate student will participate in this study and gain valuable research experience. \n\nThis study will use a large-eddy simulation (LES) dataset, consisting of two hours of 0.39m resolution data, archived at one-minute intervals. The LES data are free of non-turbulent structures typically present in the real boundary layer. The proposed LES uses a two-part sub-grid scale model to span between LES and Reynolds-average Navier-Stokes (RANS) regimes. New insights will be gained through the development of improved turbulence closure schemes, from gradient-based scaling, for single-column models.", "AwardID" -> "1500900", "Institution" -> Entity["NSFInstitution", "MarquetteUniversity"], "Investigators" -> {Entity["NSFInvestigator", "ZbigniewSorbjan"]}, "Directorate" -> "Directorate For Geosciences", "Division" -> "Div Atmospheric & Geospace Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500900&HistoricalAwards=false"], "KeywordTally" -> {{"LES", 4}, {"study", 4}, {"models", 3}, {"schemes", 3}, {"atmosphere", 2}, {"data", 2}, {"layer", 2}, {"layers", 2}, {"lowest", 2}, {"model", 2}, {"near", 2}, {"research", 2}, {"use", 2}, {"valuable", 2}, {"various", 2}}|>, "1500903" -> <|"AwardTitle" -> "Thin-Film Compound Semiconductor Photovoltaics", "AwardEffectiveDate" -> DateObject[{2015, 3, 1}], "AwardExpirationDate" -> DateObject[{2016, 2, 29}], "AwardAmount" -> Quantity[6600, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07020000", "ProgramOfficer" -> "Gregory Rorrer", "Abstract" -> "Principal Investigator: Yan\nProposal No: 1500903\n\nNontechnical Description\n\nThis symposium award will provide support for the Symposium on Thin-Film Compound Semiconductor Photovoltaics, to be held at the 2015 Materials Research Society Spring Annual Meeting. The specific goals of the symposium are to present and disseminate significant recent advances in the understanding of new materials for solar cells, and to help develop a diverse and active community of early career scientists to further technical progress in the future. \n\nTechnical Description\n\nThis symposium award will provide support for the Symposium on Thin-Film Compound Semiconductor Photovoltaics (Symposium B), to be held at the 2015 Materials Research Society Spring Annual Meeting, April 6-10, 2015, San Francisco, CA. Compound thin-film photovoltaics have demonstrated high light-to electricity conversion efficiencies, and are leading candidates to provide low-cost sustainable solar energy conversion, due to potential advantages in lowering costs for manufacturing and materials. Recent progress has improved the record efficiencies of laboratory CdTe and Cu(In,Ga)Se2 thin film solar cells considerably, reaching 21%. The topic has great importance for the materials research community to further its contribution to develop alternative energy sources. The symposium brings together a wide range of experts in research on thin-film photovoltaics, including 12 internationally recognized invited speakers, along with students and other early career scientists. There will be sessions on many different aspects of the technology, and the materials needed for production. Synergies among different materials, processing approaches, and characterization methods will be highlighted. The technical presentations on these diverse topics are designed to foster open discussion needed to advance scientific progress. The symposium will also organize a Young Scientist Tutorial to train and educate graduate and undergraduate students on the latest advances in thin-film photovoltaics.", "AwardID" -> "1500903", "Institution" -> Entity["NSFInstitution", "MaterialsResearchSociety"], "Investigators" -> {Entity["NSFInvestigator", "YanfaYan"], Entity["NSFInvestigator", "JArdieButchDillen"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Chem, Bioeng, Env, & Transp Sys", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500903&HistoricalAwards=false"], "KeywordTally" -> {{"materials", 5}, {"symposium", 5}, {"2015", 3}, {"Compound", 3}, {"photovoltaics", 3}, {"progress", 3}, {"provide", 3}, {"solar", 3}, {"Symposium", 3}, {"thin-film", 3}, {"advances", 2}, {"Annual", 2}, {"award", 2}, {"career", 2}, {"cells", 2}, {"community", 2}, {"conversion", 2}, {"Description

", 2}, {"develop", 2}, {"different", 2}, {"diverse", 2}, {"early", 2}, {"efficiencies", 2}, {"energy", 2}, {"held", 2}, {"Materials", 2}, {"Meeting", 2}, {"needed", 2}, {"Photovoltaics", 2}, {"research", 2}, {"Research", 2}, {"scientists", 2}, {"Semiconductor", 2}, {"Society", 2}, {"Spring", 2}, {"students", 2}, {"support", 2}, {"technical", 2}, {"Thin-Film", 2}}|>, "1500905" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Biome conservatism in Neotropical plant diversification? A case study in Bignoniaceae", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2017, 8, 31}], "AwardAmount" -> Quantity[20086, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010206", "ProgramOfficer" -> "Joseph Miller", "Abstract" -> "Species diversity increases latitudinally from the poles to the equator, making the tropical regions the most species rich on Earth. New World tropical plants - from Mexico to Argentina - harbor an unprecedented 37% of vascular plant species. One of the reasons for this high diversity may lie in the history of the area. South America was isolated from other continental landmasses until about 3 Mya when the isthmus of Panama closed. During this period, geological events and global climate change led to the formation and maintenance of many biomes, creating a heterogeneous landscape with new ecological opportunities for members of the isolated plant assemblage to adapt. This research will generate genetic and environmental data from a group plants with a Neotropical distribution. The goal of this work is to better understand how the evolutionary patterns in each biome combine to generate this unparalleled level of plant diversity. This work will help document existing biodiversity in the Neotropics and foster collaboration with Latin American scientists. Research findings will be communicated via publications and to the broader public by participation in museum exhibits and online media.\n\nThe focus of this work is to explore the balance of two evolutionary patterns - biome conservatism versus biome shifting- and how it has affected Neotropical plant diversification through space and time. Biome conservatism is the tendency of plant groups to remain in similar environments and retain corresponding ecological traits as they diversify. This pattern implies that evolutionary success through diversification may come primarily from biome expansion through time or long distance migration from point of origin to similar biomes. Alternatively, shifts into novel biomes- biome evolution- could be critical in driving high diversification rates by providing access to new ecological niches to which plant species can adapt. To unravel patterns of biome conservatism and biome shits in the Neotropics, field work will be conducted in Brazil and Colombia to collect members of the large Neotropical plant family Bignoniaceae. Using high-throughput amplicon-based sequencing techniques and statistical phylogenetic analyses, the goals are this project are to (A) detect early diversification events in Bignoniaceae and (B) estimate diversification rates and correlate biome conservatism and biome shift events with these diversification rates across the family. Based on the importance of niche availability to adaptation, increased opportunities available in newly occupied biomes may facilitate significant increases in speciation and diversification rate following biome shifts.", "AwardID" -> "1500905", "Institution" -> Entity["NSFInstitution", "UniversityOfWashington"], "Investigators" -> {Entity["NSFInvestigator", "RichardOlmstead"], Entity["NSFInvestigator", "AudreyRagsac"]}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500905&HistoricalAwards=false"], "KeywordTally" -> {{"biome", 10}, {"diversification", 7}, {"plant", 7}, {"biomes", 4}, {"conservatism", 4}, {"work", 4}, {"diversity", 3}, {"ecological", 3}, {"events", 3}, {"evolutionary", 3}, {"Neotropical", 3}, {"patterns", 3}, {"rates", 3}, {"species", 3}, {"adapt", 2}, {"Bignoniaceae", 2}, {"family", 2}, {"generate", 2}, {"high", 2}, {"increases", 2}, {"isolated", 2}, {"members", 2}, {"Neotropics", 2}, {"new", 2}, {"opportunities", 2}, {"plants", 2}, {"shifts", 2}, {"similar", 2}, {"time", 2}, {"tropical", 2}}|>, "1500906" -> <|"AwardTitle" -> "Descriptive set-theoretic graph theory and applications", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[153809, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "The central objects of study in this research proposal are combinatorial graphs, which are structures consisting of a underlying collection of vertices, some pairs of which are connected by edges and some pairs remaining unconnected. Despite the simplicity of this concept, familiar to any child who has played a game of connect-the-dots, graphs are sufficiently general to model many phenomena both within mathematics and also in nearby scientific disciplines. For example, graphs have found applications in computer network design, including modeling the evolution of the internet, as well as in statistical physics, including modeling atomic-scale thermodynamic interactions. In these applications, the number of vertices is so large that for analytical purposes it is indistinguishable from being infinite. In this project, the principal investigator will study infinite graphs from the descriptive set-theoretic viewpoint, in essence regarding such graphs abstractly as sets and relating the complexity of their descriptions with their concrete combinatorial properties. In areas of mathematics such as dynamics and probability, such definable graphs arise as limits of finite graphs, and the descriptive set-theoretic methods shed light on this asymptotic behavior. Additionally, the analysis finds applications within descriptive set theory as well, finding new ways of stratifying the relative difficulty of various classification problems.\n\nIn general, the objective of the project is to understand combinatorial parameters of Borel graphs on standard Borel spaces subject to various measurability constraints. For example, the chromatic number of a graph (the smallest cardinality of the image of a function assigning different values to adjacent vertices) typically has different values when the coloring function is required to be Borel, measurable with respect to some Borel probability measure, or Baire measurable with respect to some compatible Polish topology. While interesting in their own right, such parameters have (often surprising) connections with other areas of mathematics -- including combinatorial and geometric group theory, ergodic theory, probability theory, and operator algebras -- and a secondary aim of the proposal is to strengthen these connections in addition to forging new ones. More precise proposed areas of study within this general setting include: (a) existence of measurable vertex colorings, edge colorings, and matchings, (b) applications to structurability of measured equivalence relations, in particular those arising as orbit equivalence relations of probability-measure-preserving actions of locally compact Polish groups, (c) applications to the global hierarchy of Borel/measure reducibility of definable equivalence relations, especially those just above hyperfinite, (d) connections with the probabilistic aspects of graph limits.", "AwardID" -> "1500906", "Institution" -> Entity["NSFInstitution", "Carnegie-MellonUniversity"], "Investigators" -> {Entity["NSFInvestigator", "ClintonConley"]}, "ProgramElements" -> {{"Code" -> "1268", "Text" -> "FOUNDATIONS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500906&HistoricalAwards=false"], "KeywordTally" -> {{"graphs", 8}, {"applications", 5}, {"Borel", 5}, {"combinatorial", 4}, {"theory", 4}, {"areas", 3}, {"connections", 3}, {"descriptive", 3}, {"equivalence", 3}, {"general", 3}, {"including", 3}, {"mathematics", 3}, {"measurable", 3}, {"probability", 3}, {"relations", 3}, {"study", 3}, {"vertices", 3}, {"colorings", 2}, {"definable", 2}, {"different", 2}, {"example", 2}, {"function", 2}, {"graph", 2}, {"infinite", 2}, {"limits", 2}, {"measure", 2}, {"modeling", 2}, {"new", 2}, {"number", 2}, {"pairs", 2}, {"parameters", 2}, {"Polish", 2}, {"project", 2}, {"proposal", 2}, {"respect", 2}, {"set-theoretic", 2}, {"values", 2}, {"various", 2}}|>, "1500907" -> <|"AwardTitle" -> "BRIGE: A Fully Distributed Multi-Agent System Based Energy Management Solution for Microgrids", "AwardEffectiveDate" -> DateObject[{2014, 9, 1}], "AwardExpirationDate" -> DateObject[{2015, 7, 31}], "AwardAmount" -> Quantity[44898, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "07010000", "ProgramOfficer" -> "Lawrence S. Goldberg", "Abstract" -> "Intellectual Merit: Intelligent techniques are cost efficient solutions to making existing power systems smarter. To improve the reliability and energy efficiency of microgrids and lower the cost of the control system, fully distributed control solutions are preferable. As one of the most popular distributed control solutions, multi-agent systems have been widely applied for power system operation and control. However, existing solutions have limited applicability and lack rigorous stability analysis. To address the needs of microgrids and the problems with existing solutions, one of the PI?s long term research goals is to study fully distributed multi-agent system based control solutions. In this project, the PI will design three types of fully distributed optimization algorithms based on a stable global information discovery algorithm. The designed algorithms can be selected for different energy management tasks based on model availability, complexity, and response time, etc. Efficient synchronization techniques will be proposed based on analysis of agents? autonomous activities. Models with different levels of details will be developed for microgrids with multiple different types of distributed energy resources. The developed models will be used to evaluate the dynamic performances of candidate solutions and overcome the disadvantages of the optimization algorithms. The proposed algorithms can solve simple problems in real time or complex problems in several seconds or faster. Real-time simulation and experimentation will be used to investigate real world performance.\n\nBroader Impacts: This project will create new fields in power and energy research by introducing new theories and technologies. The planned work will demonstrate to power engineers that advanced computational intelligence techniques can bring about novel solutions for complex engineering problems. The success of this project will also inspire other societies with new applications and challenges. The project has potential to revolutionize the practice of power system operation by seamlessly integrating power system scheduling and control. The distributed optimization algorithms can be applied to many other large-scale online optimization and control problems. The project will generate two graduate RA positions, create two new multidisciplinary courses, and broaden participation by providing excellent hands-on learning opportunities for the large population of minority students at New Mexico State University. Outreach activities are planned to improve public awareness, understanding, and confidence of the Smart Grid. The microgrid testbed, high quality publications, and trained students produced according to this project will greatly enhance the capability of New Mexico State University in doing related research and attracting new funding from governments and industries.", "AwardID" -> "1500907", "Institution" -> Entity["NSFInstitution", "LehighUniversity"], "Investigators" -> {Entity["NSFInvestigator", "WenxinLiu"]}, "Directorate" -> "Directorate For Engineering", "Division" -> "Div Of Electrical, Commun & Cyber Sys", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500907&HistoricalAwards=false"], "KeywordTally" -> {{"solutions", 8}, {"control", 7}, {"distributed", 6}, {"power", 6}, {"project", 6}, {"algorithms", 5}, {"new", 5}, {"problems", 5}, {"system", 5}, {"based", 4}, {"energy", 4}, {"optimization", 4}, {"different", 3}, {"existing", 3}, {"fully", 3}, {"microgrids", 3}, {"research", 3}, {"techniques", 3}, {"activities", 2}, {"analysis", 2}, {"applied", 2}, {"complex", 2}, {"cost", 2}, {"create", 2}, {"developed", 2}, {"improve", 2}, {"Mexico", 2}, {"multi-agent", 2}, {"New", 2}, {"operation", 2}, {"PI", 2}, {"planned", 2}, {"proposed", 2}, {"real", 2}, {"State", 2}, {"students", 2}, {"systems", 2}, {"time", 2}, {"types", 2}, {"University", 2}, {"used", 2}}|>, "1500911" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Consequences of sympatry and allopatry for variation in reproductive genes of Drosophila pseudoobscura", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2016, 5, 31}], "AwardAmount" -> Quantity[20143, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010207", "ProgramOfficer" -> "George W. Gilchrist", "Abstract" -> "Many factors influence mate choice in both plants and animals, including choosing a mate that will provide the best quality offspring while avoiding individuals of different species. The integration of these factors into a single choice implies that traits involved in mate selection within species could be the same traits that cause species to diverge from one another. Recently, the investigators used genetically modified Drosophila melanogaster to show that the same genes that control within species mate choice are also involved in species discrimination. This project is testing this association in a natural system, to understand how different populations accumulate changes in genes that control mate choice and species discrimination. These data will provide insight into the molecular mechanisms underlying natural variation in mate choice and the formation of reproductively isolated populations, which are important factors in understanding how new species arise over evolutionary time. \n\nThe proposed research will examine DNA sequence and gene expression variation in reproductive genes in natural populations of the fruit fly Drosophila pseudoobscura, using high depth nucleotide sequencing. The experiment contrasts genetic changes that have occurred in populations that co-occur with closely related species, and thus must discriminate against them during mate choice, with changes in populations that are not exposed to other species. Analyses will assess genetic variation across all reproductive genes, as well as specifically in genes known to affect gamete competition. These variants will be associated with phenotypic data on mate choice within and between species, to differentiate genes that are important to mate choice, to species discrimination, and to both reproductive behaviors.", "AwardID" -> "1500911", "Institution" -> Entity["NSFInstitution", "IndianaUniversity"], "Investigators" -> {Entity["NSFInvestigator", "LeonieMoyle"], Entity["NSFInvestigator", "DeanCastillo"]}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500911&HistoricalAwards=false"], "KeywordTally" -> {{"species", 11}, {"mate", 9}, {"choice", 8}, {"genes", 6}, {"populations", 5}, {"changes", 3}, {"discrimination", 3}, {"factors", 3}, {"natural", 3}, {"reproductive", 3}, {"variation", 3}, {"control", 2}, {"data", 2}, {"different", 2}, {"Drosophila", 2}, {"genetic", 2}, {"important", 2}, {"involved", 2}, {"provide", 2}, {"traits", 2}}|>, "1500915" -> <|"AwardTitle" -> "Great Plains Operator Theory Symposium 2015", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2016, 4, 30}], "AwardAmount" -> Quantity[50000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This award provides funding to help defray the expenses of participants in the \"Great Plains Operator Theory Symposium 2015\" that will be held from May 26-30, 2015, on the campus of Purdue University.\n\nThis conference is the thirty-fifth installment of the Great Plains Operator Theory Symposium (GPOTS), a series that annually brings together a diverse group of mathematicians whose primary research interests are in operator theory or operator algebras. The main foci of the 2015 event are the following: classification of C*-algebras; von Neumann algebras; recent advances in operator theory; noncommutative geometry; C*-algebras and dynamical systems. The conference program provides ample opportunity for graduate students, postdocs, and other young scientists to present their work.\n\nConference web page: www.math.purdue.edu/~mdd/GPOTS2015/index.html", "AwardID" -> "1500915", "Institution" -> Entity["NSFInstitution", "PurdueUniversity"], "Investigators" -> {Entity["NSFInvestigator", "AndrewToms"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500915&HistoricalAwards=false"], "KeywordTally" -> {{"algebras", 4}, {"2015", 3}, {"operator", 3}, {"C", 2}, {"conference", 2}, {"Great", 2}, {"Operator", 2}, {"Plains", 2}, {"provides", 2}, {"Symposium", 2}, {"theory", 2}, {"Theory", 2}}|>, "1500916" -> <|"AwardTitle" -> "Topics in Fluid dynamics with free boundaries, and Kinetic theory", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[177285, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This research proposes to develop new methods to advance the current level of scientific knowledge on a diverse collection of recognized questions in a few different areas of the mathematical analysis of non-linear partial differential equations. The first part of this project involves questions regarding the dynamics of fluids, and solutions to these questions are expected to increase our understanding of water waves, tsunamis, hurricanes, and other fluid phenomena. The second part of this project studies the dynamics of plasmas from a mathematical point of view, and we anticipate that these studies will increase our understanding of the physical phenomena such as the solar wind, galactic nebulae, and the Van Allen radiations belts. The third part of this project focuses on the study the relativistic Kinetic theory and it is expected that the research will increase our physical understanding in a wide variety of places in astrophysics, for instance in high atmosphere aerodynamics where the air is a very rarefied gas and fluid equations are probably not sufficient. This project will involve training in research of postdoctoral researchers, graduate students and undergraduate students from the University of Pennsylvania and beyond, with participation of under-represented groups. The PI is working to develop innovative Active Learning Calculus courses in order to further the goal of developing a diverse and globally competitive STEM workforce and to improve STEM education at the collegiate level. \n\nThe objective of the proposed research is to fully understand both global in time existence of solutions and singularity formation of solutions when this occurs for several different fundamental physical models in non-linear partial differential equations. One part of this research is to study fluid dynamics problems with free boundaries such as the Muskat problem and the Surface Quasi-Geostrophic equations. Another part of this work looks at problems related to the relativistic Vlasov-Maxwell system which is a fundamental model of plasma physics. And a third part of this proposal will study problems on the the relativistic Boltzmann equation which is the central model in relativistic Kinetic theory. The PI proposes to develop several new methods in the Analysis of partial differential equations in the course of developing deeper understanding of these different equations. It is expected that the techniques developed to be useful for future mathematical and physical developments.", "AwardID" -> "1500916", "Institution" -> Entity["NSFInstitution", "UniversityOfPennsylvania"], "Investigators" -> {Entity["NSFInvestigator", "RobertStrain"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500916&HistoricalAwards=false"], "KeywordTally" -> {{"equations", 6}, {"research", 5}, {"physical", 4}, {"project", 4}, {"relativistic", 4}, {"understanding", 4}, {"develop", 3}, {"different", 3}, {"differential", 3}, {"dynamics", 3}, {"expected", 3}, {"fluid", 3}, {"increase", 3}, {"mathematical", 3}, {"partial", 3}, {"problems", 3}, {"questions", 3}, {"solutions", 3}, {"study", 3}, {"developing", 2}, {"diverse", 2}, {"fundamental", 2}, {"Kinetic", 2}, {"level", 2}, {"methods", 2}, {"model", 2}, {"new", 2}, {"non-linear", 2}, {"phenomena", 2}, {"PI", 2}, {"proposes", 2}, {"STEM", 2}, {"students", 2}, {"studies", 2}, {"theory", 2}, {"third", 2}}|>, "1500917" -> <|"AwardTitle" -> "Dissertation Research: Linking coexistence at local and regional scales by assessing a dormancy-dispersal tradeoff", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2017, 4, 30}], "AwardAmount" -> Quantity[20928, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010208", "ProgramOfficer" -> "George Malanson", "Abstract" -> "Understanding how and if species can coexist stably in a fragmented habitat where patches are connected by dispersal is key to understanding the maintenance of biodiversity. The coexistence of similar species?ones that feed at the same level in a food chain, have similar life histories, and share predators?requires some form of tradeoff such that each is either limited by different resources or enemies, or each is a superior competitor to the other at some points in either space, time, or both. This project will elucidate the differences in life-history strategies of two grazing zooplankton, Moina macrocopa and Daphnia pulex/pulicaria, in a freshwater rock-pools on an island off the coast of Maine, USA. The dormancy and dispersal of each species will be examined to determine if these differences promote coexistence either alone or in combination with spatial and temporal variation. This study will experimentally test whether one species is superior at remaining dormant while one species is superior at dispersing, and will model whether or not this allows these two species to coexist. This project will train one Ph.D. student and multiple undergraduate students through field-assistantships and mentored independent projects. The research will be communicated to the public, K-12 students, and undergraduates from many institutions at a nearby biological field station. The research itself promotes the progress of science and has implications for national welfare through application to the management of biodiversity of fragmented habitats; the project also supports education and diversity.\n\nUnderstanding how and if species can coexist stably in a fragmented habitat is key to understanding the maintenance of biodiversity. The coexistence of similar species?ones that feed at the same trophic level, have similar life histories, and share predators?requires some form of tradeoff such that each is either limited by different resources or enemies, or each is a superior competitor to the other at some points in either space, time, or both. The differences in life-history strategies of two grazing zooplankton, Moina macrocopa and Daphnia pulex/pulicaria, will be elucidated for a freshwater rock-pool metacommunity on an island off the coast of Maine, USA. Life history strategies relating to dormancy and dispersal of each species will be examined and used to determine if these differences promote coexistence either alone or in combination with spatial and temporal variation. This study will experimentally test (1) whether one species is superior at remaining dormant while one species is superior at dispersing, and (2) whether or not this allows these two species to coexist in this metacommunity by measuring the necessary relationships to parameterize a mathematical dormancy-dispersal model to test the conditions for coexistence. The spatial and temporal dispersal rates of diapausing eggs and their establishment success will be measured by stocking focal pools surrounded by other pools in which the species are initially absent. These data will be combined with data on competition outcomes in both artificial mesocosms and manipulated rock pools. In addition to furthering our understanding of the maintenance of biodiversity, which can be applied to the management of naturally and anthropogenically fragmented habitats, this project will train one Ph.D. student and multiple undergraduate students through field-assistantships and mentored independent projects. Furthermore, the information about this project will be disseminated to visitors to Shoals Marine Laboratory, which includes the public, K-12 students, and undergraduates from many institutions.", "AwardID" -> "1500917", "Institution" -> Entity["NSFInstitution", "CornellUniversity"], "Investigators" -> {Entity["NSFInvestigator", "NelsonHairston"], Entity["NSFInvestigator", "KatherineSirianni"]}, "ProgramElements" -> {{"Code" -> "1182", "Text" -> "POP & COMMUNITY ECOL PROG"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500917&HistoricalAwards=false"], "KeywordTally" -> {{"species", 13}, {"superior", 6}, {"coexistence", 5}, {"project", 5}, {"biodiversity", 4}, {"coexist", 4}, {"differences", 4}, {"dispersal", 4}, {"fragmented", 4}, {"similar", 4}, {"students", 4}, {"maintenance", 3}, {"pools", 3}, {"spatial", 3}, {"strategies", 3}, {"temporal", 3}, {"test", 3}, {"understanding", 3}, {"allows", 2}, {"coast", 2}, {"combination", 2}, {"competitor", 2}, {"Daphnia", 2}, {"data", 2}, {"determine", 2}, {"different", 2}, {"dispersing", 2}, {"dormancy", 2}, {"dormant", 2}, {"enemies", 2}, {"examined", 2}, {"experimentally", 2}, {"feed", 2}, {"field-assistantships", 2}, {"form", 2}, {"freshwater", 2}, {"grazing", 2}, {"habitat", 2}, {"habitats", 2}, {"histories", 2}, {"independent", 2}, {"institutions", 2}, {"island", 2}, {"K-12", 2}, {"key", 2}, {"level", 2}, {"life", 2}, {"life-history", 2}, {"limited", 2}, {"macrocopa", 2}, {"Maine", 2}, {"management", 2}, {"mentored", 2}, {"metacommunity", 2}, {"model", 2}, {"Moina", 2}, {"multiple", 2}, {"ones", 2}, {"Ph.D.", 2}, {"points", 2}, {"predators", 2}, {"projects", 2}, {"promote", 2}, {"public", 2}, {"pulex", 2}, {"pulicaria", 2}, {"remaining", 2}, {"requires", 2}, {"research", 2}, {"resources", 2}, {"share", 2}, {"space", 2}, {"stably", 2}, {"student", 2}, {"study", 2}, {"time", 2}, {"tradeoff", 2}, {"train", 2}, {"undergraduate", 2}, {"undergraduates", 2}, {"USA", 2}, {"variation", 2}, {"zooplankton", 2}}|>, "1500919" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Effect of niche conservation versus niche evolution on diversification rate in the Neotropical plant genus Citharexylum (Verbenaceae)", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2017, 6, 30}], "AwardAmount" -> Quantity[20085, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010206", "ProgramOfficer" -> "Simon Malcomber", "Abstract" -> "The Neotropics are estimated to house more seed plant species than the African, Asian, and Oceanic tropics combined. Recent studies of diverse plant groups have noted that closely related species often occupy similar types of habitats despite being geographically separated. This observation led to the hypothesis that dispersal is common in many groups and that migration to new, but suitable habitats can spur diversification. Adaptations can also stimulate radiations within plant groups, though less is known about the contributions of these seemingly rare but important evolutionary events to biodiversity. This research will focus on the systematics of the Neotropical plant genus Citharexylum (Verbenaceae), and the relative contributions of dispersal and adaptation to species diversification in the group. Studies that provide an understanding of how organisms have dispersed and evolved in the past provide the necessary historical context to predict how these same groups are likely to disperse and diversify in the future. One graduate student will be trained and undergraduates will be introduced to a broad range of laboratory and analytical methods. The research will also enhance international scientific research infrastructure by establishing collaborations in several South and Central American countries. .\n\nThe object of this project is to understand how biogeographic events (migration/colonization versus adaptation) influence diversification in Neotropical plant lineages. This study will elucidate the biogeographic history of the plant genus Citharexylum, a lineage of trees and shrubs that originated in and diversified into multiple biomes of the Neotropics. A time-calibrated phylogeny of Citharexylum with near-complete sampling will be inferred using multiple, independent loci. Phylogenetic inference will take a two-tiered approach using both high-throughput and traditional sequencing methods to produce a robust phylogeny. This framework will then be used to test evolutionary and biogeographic hypotheses about the genus. Statistical analyses will reconstruct ancestral ranges/climatic niches and detect the placement and magnitude of diversification rate shifts in the phylogeny. Additionally, the phylogeny will be dated using a fossil-calibrated phylogeny of the inclusive group Lamiales allowing assessment of migrations and adaptive events with known geologic and climatic events in the history of the Neotropics. This work will help build the foundation of knowledge surrounding the timing and magnitude of diversification events as well as the directionality of niche evolution in the New World.", "AwardID" -> "1500919", "Institution" -> Entity["NSFInstitution", "UniversityOfWashington"], "Investigators" -> {Entity["NSFInvestigator", "RichardOlmstead"], Entity["NSFInvestigator", "LauraFrost::myfv3"]}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500919&HistoricalAwards=false"], "KeywordTally" -> {{"plant", 6}, {"diversification", 5}, {"events", 5}, {"phylogeny", 5}, {"groups", 4}, {"biogeographic", 3}, {"Citharexylum", 3}, {"genus", 3}, {"Neotropics", 3}, {"research", 3}, {"species", 3}, {"using", 3}, {"adaptation", 2}, {"climatic", 2}, {"contributions", 2}, {"dispersal", 2}, {"evolutionary", 2}, {"group", 2}, {"habitats", 2}, {"history", 2}, {"known", 2}, {"magnitude", 2}, {"methods", 2}, {"migration", 2}, {"multiple", 2}, {"Neotropical", 2}, {"provide", 2}}|>, "1500920" -> <|"AwardTitle" -> "Model Theory, Difference/Differential Equations, and Applications", "AwardEffectiveDate" -> DateObject[{2015, 3, 15}], "AwardExpirationDate" -> DateObject[{2016, 2, 29}], "AwardAmount" -> Quantity[34999, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This project supports participation by US-based researchers, particularly speakers, organizers, graduate students, and recent PhD recipients, at the conference \"Model Theory, Difference/Differential Equations, and Applications\" held at CIRM in Luminy, France, April 7th - 10th, 2015. This conference brings together researchers in model theory, in difference and differential algebra, and in allied fields (such as algebraic dynamics) in which theorems from model theoretic algebra have been applied. This workshop will foster research interactions and will provide an informal setting for graduate students and younger researchers to learn of the newest trends in this research area and interact with some of the most prominent researchers around the world. \n\nIn particular, this project will provide financial support to a substantial number of graduate students and young researchers from the United States. Differential algebraic geometry, differential Galois theory and, more recently, algebraic dynamics have benefited from the close interaction with model theory, especially the model theory of fields with operators. The conference aims to catalyze further developments in this area. Details about the conference may be found at http://scientific-events.weebly.com/1194.html .", "AwardID" -> "1500920", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-Berkeley"], "Investigators" -> {Entity["NSFInvestigator", "ThomasScanlon"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500920&HistoricalAwards=false"], "KeywordTally" -> {{"researchers", 5}, {"conference", 4}, {"model", 4}, {"theory", 4}, {"algebraic", 3}, {"graduate", 3}, {"students", 3}, {"algebra", 2}, {"area", 2}, {"differential", 2}, {"Differential", 2}, {"dynamics", 2}, {"fields", 2}, {"project", 2}, {"provide", 2}, {"research", 2}}|>, "1500922" -> <|"AwardTitle" -> "Noncommutative Multivariable Operator Theory", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[116071, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Many problems in the physical sciences and engineering can be modeled by noncommutative functions. Such functions are used to encode information about physical systems, so studying various aspects of them could reveal important information about how to design systems that perform desired tasks or how to maximize their performance. The motivation for this project is the relatively recent worldwide interest in the noncommutative aspects of multivariable operator theory and function theory, and their interplay with the classical theory of functions, algebras, and harmonic analysis. The present project aims at extending fundamental ideas from analysis, algebra, and geometry to the noncommutative context and finding applications in science and engineering. The study of noncommutative functions and the algebras that they generate, which is the goal of the project, has potential applications to free probability, interpolation , optimization and control, and systems theory. The principal investigator expects the results of the project to make new connections between several areas of mathematics and to have applications in mathematical physics. Another important objective of the project is to attract graduate students to the PI's research program and help build a Ph.D. program in mathematics at the University of Texas-San Antonio. \n\nThe proposed project is a continuation of the ongoing program of the principal investigator to develop a free analogue of the Sz.-Nagy-Foias theory of contractions for noncommutative domains and varieties in several noncommuting variables and to develop the theory of free holomorphic functions on these domains. The project is devoted to enhancing the understanding of the structure of the noncommutative polydomains and varieties that admit universal models and have rich analytic function theory, and to make advances towards their classification up to free biholomorphic equivalence. This is accompanied by the study of free holomorphic functions on these polydomains with the emphasis on geometric aspects and the connection with the hyperbolic geometry. The most prominent feature of this project is the interaction between the structure of the noncommutative polydomains and varieties, the operator algebras generated by the corresponding universal model operators, and the noncommutative analytic function theory on these polydomains. Moreover, this study is anchored in classical complex function theory in several variables and in complex algebraic geometry. The project focuses on the following problems: classification of noncommutative polydomains and varieties up to free biholomorphic equivalence and the classification of the associated universal algebras up to completely isometric isomorphisms; universal models, invariant subspaces, and commutant lifting; unitary invariants on noncommutative polydomains (e.g., the curvature, the Euler characteristic, and the entropy); hyperbolic geometry on noncommutative polyballs; free holomorphic functions on polydomains; free holomorphic self-maps of noncommutative balls and composition operators.", "AwardID" -> "1500922", "Institution" -> Entity["NSFInstitution", "UniversityOfTexasAtSanAntonio"], "Investigators" -> {Entity["NSFInvestigator", "GeluPopescu"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500922&HistoricalAwards=false"], "KeywordTally" -> {{"noncommutative", 12}, {"project", 9}, {"theory", 9}, {"free", 8}, {"functions", 7}, {"polydomains", 7}, {"algebras", 4}, {"function", 4}, {"geometry", 4}, {"holomorphic", 4}, {"universal", 4}, {"varieties", 4}, {"applications", 3}, {"aspects", 3}, {"classification", 3}, {"program", 3}, {"study", 3}, {"systems", 3}, {"analysis", 2}, {"analytic", 2}, {"biholomorphic", 2}, {"classical", 2}, {"complex", 2}, {"develop", 2}, {"domains", 2}, {"engineering", 2}, {"equivalence", 2}, {"hyperbolic", 2}, {"important", 2}, {"information", 2}, {"investigator", 2}, {"make", 2}, {"mathematics", 2}, {"models", 2}, {"operator", 2}, {"operators", 2}, {"physical", 2}, {"principal", 2}, {"problems", 2}, {"structure", 2}, {"variables", 2}}|>, "1500925" -> <|"AwardTitle" -> "Existence of Solutions to Hyperbolic Differential Equations in Mathematical Physics", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[99999, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The PI's research concerns basic mathematical questions about systems of nonlinear hyperbolic differential equations in mathematical physics. These include many important equations in classical field theory and continuum mechanics; e.g. Einstein's equations of general relativity and Euler's equations of fluids. The basic questions concern existence, uniqueness and stability of solutions, as well as the question if solutions blow up (e.g. black holes in general relativity) and if not what the long time behavior of solutions are? More specifically, the PI is mainly working in two areas. One project is to study if Einstein's and related equations have solutions for all times or if the solutions blow up. A long term goal is to study the stability of large solutions like black holes and the big bang in general relativity. The motivation is to understand the large scale structure of our universe. The Physicists are building large gravitational wave detectors to observe the universe and the theory has to be developed together with observations. Another project is to study a class of problems that occur in fluid dynamics and general relativity, in particular, proving existence and stability for the free boundary problem of the motion of the surface of a fluid in vacuum (such as the surface of the ocean). A long term goal is to study the long time behavior of astrophysical bodies such as gaseous stars as well as other interface problems of fluids and solids. It is conceivable that understanding the properties of and controlling the interface between two fluids could have important applications. In particular there is a version of the problem in magneto-hydrodynamics and controlling the plasma is needed for constructing fusion reactors.\n\nTo solve these problems the PI and collaborators are developing new techniques that could be useful for studying many other problems as well. In particular, they are using geometric methods combined with frequency decomposition methods to study hyperbolic differential equations. The PI's and collaborator's greatly simplified existence proof for Einstein's equations and its generalizations and refinements will have a large impact. Moreover the detailed asymptotic behavior they prove in harmonic coordinates will be useful also for the physics community. The methods the PI has developed for the free boundary problem of fluids work also for the compressible case and also with vorticity since it uses interior equations and not just equations on the boundary. The methods PI and collaborators are developing to deal with nonlinear equations with variable coefficients will hopefully also be useful to show stability of perturbations of large solutions.", "AwardID" -> "1500925", "Institution" -> Entity["NSFInstitution", "JohnsHopkinsUniversity"], "Investigators" -> {Entity["NSFInvestigator", "HansLindblad"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500925&HistoricalAwards=false"], "KeywordTally" -> {{"equations", 10}, {"solutions", 7}, {"large", 5}, {"study", 5}, {"fluids", 4}, {"general", 4}, {"long", 4}, {"methods", 4}, {"PI", 4}, {"problems", 4}, {"relativity", 4}, {"stability", 4}, {"behavior", 3}, {"boundary", 3}, {"Einstein's", 3}, {"existence", 3}, {"particular", 3}, {"problem", 3}, {"useful", 3}, {"basic", 2}, {"black", 2}, {"blow", 2}, {"collaborators", 2}, {"controlling", 2}, {"developed", 2}, {"developing", 2}, {"differential", 2}, {"e.g.", 2}, {"fluid", 2}, {"free", 2}, {"goal", 2}, {"holes", 2}, {"hyperbolic", 2}, {"important", 2}, {"interface", 2}, {"mathematical", 2}, {"nonlinear", 2}, {"physics", 2}, {"PI's", 2}, {"project", 2}, {"questions", 2}, {"surface", 2}, {"term", 2}, {"theory", 2}, {"time", 2}, {"universe", 2}}|>, "1500926" -> <|"AwardTitle" -> "Annual Spring Institute on Noncommutative Geometry and Operator Algebras (NCGOA) 2015", "AwardEffectiveDate" -> DateObject[{2015, 4, 1}], "AwardExpirationDate" -> DateObject[{2016, 3, 31}], "AwardAmount" -> Quantity[38200, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This award provides funding to help defray the expenses of participants in the \"Annual Spring Institute on Noncommutative Geometry and Operator Algebras 2015\" that will be held from May 1-7, 2015, on the campus of Vanderbilt University. The field of classic geometry studies geometric objects whose coordinates commute. Noncommutative geometry is a mathematical theory specifically designed to handle \"geometric\" objects whose coordinates do not commute but which do occur naturally in both mathematics and physics. Such \"noncommutative spaces\" naturally arise in quantum physics, analysis, topology and geometry of manifolds, and number theory. Noncommutative geometry provides the tools to analyze and compute with these spaces, and it has led to important applications in the geometry and topology of manifolds, mathematical physics, knot theory, statistical mechanics, and conformal field theory. The annual Spring Institute includes a school specifically designed to highlight the most significant recent advances in noncommutative geometry and operator algebras, to identify new emerging directions, and to help graduate students and postdocs learn the fundamentals of this broad and technically difficult subject and navigate to the research frontiers.\n\nThis event is the thirteenth installment of the Vanderbilt Noncommutative Geometry and Operator Algebra (NCGOA) spring conferences, a series that each year brings together a diverse group of roughly one hundred mathematicians whose primary research interests are in operator algebras and related topics. The main focus of the 2015 event is on operator algebras and approximation properties of groups. The conference program, which includes five mini-courses and twenty lectures by world leaders in the field, provides ample opportunity for graduate students, postdocs, and other young scientists to present their work. \n\nConference web site: https://my.vanderbilt.edu/ncgoa15/", "AwardID" -> "1500926", "Institution" -> Entity["NSFInstitution", "VanderbiltUniversity"], "Investigators" -> {Entity["NSFInvestigator", "VaughanJones"], Entity["NSFInvestigator", "DietmarBisch"], Entity["NSFInvestigator", "JessePeterson"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500926&HistoricalAwards=false"], "KeywordTally" -> {{"geometry", 6}, {"Noncommutative", 4}, {"theory", 4}, {"2015", 3}, {"algebras", 3}, {"field", 3}, {"operator", 3}, {"physics", 3}, {"provides", 3}, {"commute", 2}, {"coordinates", 2}, {"designed", 2}, {"event", 2}, {"geometric", 2}, {"Geometry", 2}, {"graduate", 2}, {"help", 2}, {"includes", 2}, {"Institute", 2}, {"manifolds", 2}, {"mathematical", 2}, {"naturally", 2}, {"noncommutative", 2}, {"objects", 2}, {"Operator", 2}, {"postdocs", 2}, {"research", 2}, {"spaces", 2}, {"specifically", 2}, {"Spring", 2}, {"students", 2}, {"topology", 2}, {"Vanderbilt", 2}}|>, "1500931" -> <|"AwardTitle" -> "Methane release from thermokarst lakes: Thresholds and feedbacks in the lake to watershed hydrology-permafrost system", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[2086836, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "06090100", "ProgramOfficer" -> "Neil R. Swanberg", "Abstract" -> "Nontechnical\n\nMethane is an important greenhouse gas, much more so than carbon dioxide over the short term. There is a lot of it in frozen ground, called permafrost, in the Arctic that can be released as the permafrost thaws, so warming in the Arctic can lead to more warming, a so-called positive feedback. Understanding such feedbacks is an important part of understanding how the arctic system works. Much of this process occurs at the bottoms of lakes, where some of the methane is frozen in lake sediments beneath the lake, but some also comes from under the permafrost deep under the lake. Methane release from the sub-permafrost environment under lakes would be a new and poorly understood feedback to the climate system.\n\nThis project is a first step in exploring these processes within the hydrology-permafrost-methane lake-to-watershed system to inform future biogeochemical models for methane release. Since lakes in areas of discontinuous permafrost are common, the proposed study domain will offer process-oriented insights that are applicable across the Arctic.\n\nThe project will also train postdocs, graduate and undergraduate students and support an early-career scientist. In addition there will be outreach to science teachers and their students in fieldwork and classroom activities on lakes and integration of results into K-G12 curriculum through the National Geographic Society's Learning program, and to millions of National Geographic magazine readers, television viewers and K- G12 students. Further, the efforts will contribute to the Alaska Geological and Hydrological Survey program to develop a detailed understanding of Alaska's groundwater systems via the central involvement of the Alaska Geological and Geophysical Survey.\n\nTechnical\n\nUncertainties in the budget of atmospheric methane (CH4), an important greenhouse gas released by thermokarst lakes, limit the accuracy of climate change projections. The objective of this grant is to refine climate feedback representations by integrating permafrost-hydrology-methane processes across scales (thermokarst-lake to watershed). Methane release from thermokarst lakes is typically considered to be solely derived from the lake and its talik (thaw bulb beneath the lake), while not accounting for the production, storage, and potential escape of CH4 beneath the permafrost. A rugged permafrost bottom is proposed to favor gas storage in hollow \"pockets\", which can rapidly release large sub(below)- permafrost CH4 stores when an open-talik forms that connects the sub-permafrost to the supra(above)- permafrost environment. Groundwater flow could accelerate thaw and therefore enhance CH4 formation and release. Model experiments informed by field measurements and laboratory analyses at Goldstream Valley, Interior Alaska, will test the hypothesis that the coupled hydrology-permafrost-methane system releases more CH4 than a scenario with static hydrology and only supra-permafrost CH4 sources. The resulting radiative forcing will be quantified via conceptual modeling, also informed by field measurements and laboratory analyses, to include talik and sub-permafrost CH4 and CO2 emissions, anaerobic oxidation of sub-permafrost CH4, and CO2 uptake and sequestration as lake sediments form peat. In addition to a watershed-scale quantification, a first order estimation of the sub-permafrost derived radiative forcing will be provided for the pan-arctic discontinuous permafrost domain of yedoma (organic-rich, Pleistocene-aged, loess-dominated permafrost).", "AwardID" -> "1500931", "Institution" -> Entity["NSFInstitution", "UniversityOfAlaskaFairbanksCampus"], "Investigators" -> {Entity["NSFInvestigator", "VladimirRomanovsky"], Entity["NSFInvestigator", "DavidBarnes::mnb5n"], Entity["NSFInvestigator", "KateyWalter"], Entity["NSFInvestigator", "AnnaLiljedahl"]}, "ProgramElements" -> {{"Code" -> "5219", "Text" -> "ARCTIC SYSTEM SCIENCE PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "1079", "Text" -> "ARCTIC RESEARCH"}}, "Directorate" -> "Directorate For Geosciences", "Division" -> "Division Of Polar Programs", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500931&HistoricalAwards=false"], "KeywordTally" -> {{"permafrost", 10}, {"CH4", 8}, {"lake", 6}, {"lakes", 6}, {"release", 5}, {"sub-permafrost", 5}, {"Alaska", 3}, {"beneath", 3}, {"climate", 3}, {"feedback", 3}, {"gas", 3}, {"important", 3}, {"methane", 3}, {"students", 3}, {"system", 3}, {"addition", 2}, {"analyses", 2}, {"Arctic", 2}, {"CO2", 2}, {"derived", 2}, {"discontinuous", 2}, {"domain", 2}, {"environment", 2}, {"field", 2}, {"forcing", 2}, {"frozen", 2}, {"Geographic", 2}, {"Geological", 2}, {"greenhouse", 2}, {"hydrology-permafrost-methane", 2}, {"informed", 2}, {"laboratory", 2}, {"measurements", 2}, {"Methane", 2}, {"National", 2}, {"processes", 2}, {"program", 2}, {"project", 2}, {"proposed", 2}, {"radiative", 2}, {"released", 2}, {"sediments", 2}, {"storage", 2}, {"talik", 2}, {"thaw", 2}, {"thermokarst", 2}, {"understanding", 2}, {"via", 2}, {"warming", 2}}|>, "1500933" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Hybrid zone formation and comparative genomic divergences in South American lizards (Iguania: Liolaemidae)", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 5, 31}], "AwardAmount" -> Quantity[16304, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010206", "ProgramOfficer" -> "Simon Malcomber", "Abstract" -> "Hybrid zones are geographical areas where hybrid offspring have mixed genetic composition and physical appearances compared to their parent populations/species. By studying genomic divergence in hybrid zones, researchers can better understand which differences are responsible for the formation of new species, and also the genomic regions that separate species. Such knowledge is relevant to many fields beyond systematics, including ecology, conservation biology, and even agriculture. This research project focuses on species within the South American lizard genus, Liolaemus, and uses genomic tools to investigate the age of hybrid zones, how they form, and how natural and sexual selection maintain genetic boundaries. Although many hybrid zones have been studied in northern temperate systems, southern temperate systems have received comparatively little attention. This research will train one graduate student in diverse systematic methods and undergraduates in field, laboratory and analytical methods. The project will also enhance international scientific infrastructure through collaborations with Argentinian researchers. Results from this research will be broadly disseminated through displays and presentations at the Burke Museum of Natural History and Culture in Seattle, WA.\n\nThe proposed research will investigate hybridization and comparative species divergences across three species pairs in the Liolaemus fitzingerii group. In part, the hypothesis will be tested that these hybrid zones have formed due to secondary contact following post-glacial range expansions approximately 12,000 years ago. Genome-wide single nucleotide polymorphism (SNP) data will be generated using the restriction site-associated DNA sequencing (RADseq) method to estimate the genetic and geographic transitions between species in three separate hybrid zones. SNP data will also be used to estimate evolutionary relationships and delimit species. Aligning the SNP data to an annotated genome will enable the identification of regions of the genome that are involved in maintaining species boundaries in this group. Together, these data will shed new light on the genomic changes that occur within hybrid zones, and provide novel insights into the mechanisms driving the formation of new species.", "AwardID" -> "1500933", "Institution" -> Entity["NSFInstitution", "UniversityOfWashington"], "Investigators" -> {Entity["NSFInvestigator", "AdamLeache"], Entity["NSFInvestigator", "JaredGrummer"]}, "ProgramElements" -> {{"Code" -> "1171", "Text" -> "PHYLOGENETIC SYSTEMATICS"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500933&HistoricalAwards=false"], "KeywordTally" -> {{"species", 10}, {"hybrid", 7}, {"zones", 7}, {"data", 4}, {"genomic", 4}, {"research", 4}, {"genetic", 3}, {"new", 3}, {"SNP", 3}, {"boundaries", 2}, {"estimate", 2}, {"formation", 2}, {"genome", 2}, {"group", 2}, {"investigate", 2}, {"Liolaemus", 2}, {"methods", 2}, {"project", 2}, {"regions", 2}, {"researchers", 2}, {"separate", 2}, {"systems", 2}, {"temperate", 2}}|>, "1500939" -> <|"AwardTitle" -> "Conference on Recent Developments in Continuum Mechanics and Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 3, 15}], "AwardExpirationDate" -> DateObject[{2016, 2, 29}], "AwardAmount" -> Quantity[18250, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Eugene Gartland", "Abstract" -> "This award provides partial support for participants in the \"Conference on Recent Developments in Continuum Mechanics and Partial Differential Equations\" held at the University of Nebraska-Lincoln (UNL), April 18-19, 2015. The subject of continuum mechanics is concerned with modeling the mechanical behavior of materials as continua: solids (elasticity) and liquids (fluid dynamics). It underlies numerous engineering applications, including the behavior of architectural structures, tires and other vehicle parts, aerospace vehicles, and a wide range of other deformable substances. Partial differential equations provide a mathematical language for expressing relationships among quantities of interest, such as the distortion of an elastic body or the velocity in a fluid, and most mathematical models in engineering and science are expressed in terms of partial differential equations. This meeting will be held in conjunction with the Howard Rowlee Lecture, an endowed public lecture presented annually by the Department of Mathematics at UNL. This year's lecture will be given on April 17th, and the timing and coordination of the Lecture and the Conference should enhance the impact of both. The purpose of the Conference is to foster contacts between mathematicians (junior, senior, and all points in between) within a broad spectrum of applied mathematics.\n\nThe Conference will comprise a series of presentations by established, prominent researchers, as well as recent Ph.D. recipients. The meeting brings together specialists who, owing to their respective fields of study, might not otherwise have occasion to meet and exchange ideas. The meeting will focus on recent advances in continuum mechanics, partial differential equations, and related fields in applied mathematics. The interests of the speakers cover areas such as numerical analysis, variational problems, mathematical modeling, singular integrals, pseudo-differential operators, dispersive equations, and nonlinear acoustics. The lectures will address some of the major problems in these fields, including modeling aspects, and analytic and numerical results. They will also present new techniques that have been recently developed, as well as open problems and possible venues for their investigation. \n\nConference web site: http://www.math.unl.edu/~mfoss3/2015conference/", "AwardID" -> "1500939", "Institution" -> Entity["NSFInstitution", "UniversityOfNebraska-Lincoln"], "Investigators" -> {Entity["NSFInvestigator", "MikilFoss"], Entity["NSFInvestigator", "PetronelaRadu"]}, "ProgramElements" -> {{"Code" -> "1266", "Text" -> "APPLIED MATHEMATICS"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500939&HistoricalAwards=false"], "KeywordTally" -> {{"Conference", 4}, {"equations", 4}, {"differential", 3}, {"fields", 3}, {"mathematical", 3}, {"meeting", 3}, {"modeling", 3}, {"partial", 3}, {"problems", 3}, {"applied", 2}, {"April", 2}, {"behavior", 2}, {"continuum", 2}, {"engineering", 2}, {"fluid", 2}, {"held", 2}, {"including", 2}, {"lecture", 2}, {"Lecture", 2}, {"mechanics", 2}, {"numerical", 2}, {"Partial", 2}, {"recent", 2}, {"UNL", 2}}|>, "1500943" -> <|"AwardTitle" -> "Invariant objects in dynamical systems: Analysis and numerics", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[125000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "Many problems in the natural sciences are modeled by a system with a simple rule that gives the next state of the system as a function of the present one. It has become increasingly apparent that many of these rules lead to complicated behavior when applied repeatedly. This complicated behavior is often called \"chaos\". To understand the behavior of a system and make useful predictions is a deep mathematical problem. One possible approach is to find \"landmarks\". A landmark is a small subsystem that behaves in a simple manner and which anchors the behavior of the system. If enough of these landmarks can be found, they can provide a skeleton for the dynamics which gives a global understanding of the system itself. \n\nThe plan is to develop systematic and accurate methods for the calculation of landmarks. Another goal is to prove theorems which show that the calculations satisfying some conditions are correct. It is planned to obtain results which show that if certain landmarks are found in some configurations (which can be verified with finite accuracy calculations) then conclusions can be obtained for all times. The hope is to make contact with concrete problems motivated by questions in solid state physics and chemistry. The work in the project will also be used as a training ground for graduate students, postdocs and visitors. For over 50 years, the most commonly used landmarks in dynamical systems have been normally hyperbolic manifolds and quasi-periodic orbits as well as their stable and unstable manifolds. Here, it is proposed to develop a systematic way of computing these objects theoretically as well as numerically. Another goal is to prove constructive existence theorems that validate approximate solutions and also to develop and implement fast and accurate algorithms. The unifying principle is to look for functional equations that describe the invariance and then use a variety of methods to try to solve them. The methods will vary from geometry to functional analysis. A further part of the proposed work is to begin studying special solutions in some infinite dimensional problems including partial differential equations and delay differential equations with state dependent delays.", "AwardID" -> "1500943", "Institution" -> Entity["NSFInstitution", "GeorgiaTechResearchCorporation"], "Investigators" -> {Entity["NSFInvestigator", "RafaelDeLaLlave"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500943&HistoricalAwards=false"], "KeywordTally" -> {{"landmarks", 5}, {"system", 5}, {"behavior", 4}, {"develop", 3}, {"equations", 3}, {"methods", 3}, {"problems", 3}, {"state", 3}, {"accurate", 2}, {"calculations", 2}, {"complicated", 2}, {"differential", 2}, {"found", 2}, {"functional", 2}, {"gives", 2}, {"goal", 2}, {"make", 2}, {"manifolds", 2}, {"proposed", 2}, {"prove", 2}, {"simple", 2}, {"solutions", 2}, {"systematic", 2}, {"theorems", 2}, {"used", 2}, {"work", 2}}|>, "1500944" -> <|"AwardTitle" -> "Anti-Concentration, Random Structures, and Sumsets", "AwardEffectiveDate" -> DateObject[{2015, 6, 15}], "AwardExpirationDate" -> DateObject[{2019, 5, 31}], "AwardAmount" -> Quantity[150000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "In this project, the goal is to investigate the distribution of random variables arising from practical problems such as solving linear systems of equations or finding the roots of high degree polynomials. These problems are critical in many developments in computer science and engineering. Finding roots of a polynomial is, in particular, a classical and fundamental problem with widespread applications. The main focus of the project is to prove that many natural distributions of random variables do not have large mass on a single point. With this new tool, the investigator hopes to provide answers to long-standing questions such as: In a typical case, how many roots of a polynomial of degree n are real? \n\nThe principal investigator aims to develop a theory for the anti-concentration phenomenon. Anti-concentration inequalities have been playing an important role in many areas where probability is involved. Recent new insights in the field have led to a significant refinement of several classical results with a broad range of applications. The investigator plans to extend the new results to a more general (nonlinear) setting. Achievements in this direction will have an immediate impact in different fields. Another part of the project continues the study of random discrete structures, in particular, random matrices and random polynomials. The PI will investigate various basic problems, such as properties and distribution of random determinants, the non-existence of multiple eigenvalues and its relation to the QR algorithm, and the classical question: How many roots of a random polynomial are real? He will also investigate sum-set problems in additive combinatorics (for example, an old question of Erdos and Moser on sum-free sets in a group).", "AwardID" -> "1500944", "Institution" -> Entity["NSFInstitution", "YaleUniversity"], "Investigators" -> {Entity["NSFInvestigator", "VanVu"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500944&HistoricalAwards=false"], "KeywordTally" -> {{"random", 7}, {"problems", 4}, {"roots", 4}, {"classical", 3}, {"investigate", 3}, {"investigator", 3}, {"new", 3}, {"polynomial", 3}, {"project", 3}, {"applications", 2}, {"degree", 2}, {"distribution", 2}, {"particular", 2}, {"polynomials", 2}, {"question", 2}, {"real", 2}, {"results", 2}, {"variables", 2}}|>, "1500947" -> <|"AwardTitle" -> "Measure Theory and Geometric Topology in Dynamics", "AwardEffectiveDate" -> DateObject[{2015, 5, 15}], "AwardExpirationDate" -> DateObject[{2018, 4, 30}], "AwardAmount" -> Quantity[99405, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "The goal of Dynamical Systems theory is to describe the long run behavior of a body or of a collection of particles subject to laws of motion. It is often the case that full knowledge of the particles' position and velocity are not exact. As a particle moves after a unit of time (say a day), the new position is not known exactly. In this project such systems are studied. The goal is to show that the long run behavior of the collection of particles is governed by some probability distribution in the phase space. The distribution should have nice geometric properties. While the \"chaotic\" behavior of these system is by definition impossible to be exactly predicted there are systems which are described by algebraic equations where researchers can probabilistically study the long run behavior.\n\nThe random iteration of diffeomorphisms is an important model for different types of dynamical systems. The PI plans to study these random iterations and gives a precise (as precise as possible) description of the stationary measure associated with it, particularly its geometric properties. Once geometric properties are established, some statistical properties can be deduced as corollaries, for example, the equidistribution of almost every orbit with respect to volume. This project will develop in two additional directions. One concerns dynamical systems with multidimensional time (i.e. actions of higher rank groups) and the other concerns classical dynamical systems (i.e. one dimensional time) displaying some uniform (though possibly partial) hyperbolicity. The unifying theme in the study is the techniques used which involve the interactions between measure theoretical and topological properties of a system. In all cases a description of relevant invariant measures is desired, how this impacts the topological dynamics and ultimately how this affects the topology of the ambient manifold. The PI also seeks intermediate interactions, for instance how the topology of the manifold imposes restrictions on the dynamics.", "AwardID" -> "1500947", "Institution" -> Entity["NSFInstitution", "PennsylvaniaStateUnivUniversityPark"], "Investigators" -> {Entity["NSFInvestigator", "FedericoRodriguezHertz"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500947&HistoricalAwards=false"], "KeywordTally" -> {{"properties", 5}, {"systems", 5}, {"behavior", 3}, {"dynamical", 3}, {"geometric", 3}, {"long", 3}, {"particles", 3}, {"run", 3}, {"study", 3}, {"time", 3}, {"collection", 2}, {"concerns", 2}, {"description", 2}, {"distribution", 2}, {"dynamics", 2}, {".e.", 2}, {"exactly", 2}, {"goal", 2}, {"interactions", 2}, {"manifold", 2}, {"measure", 2}, {"PI", 2}, {"position", 2}, {"precise", 2}, {"project", 2}, {"random", 2}, {"system", 2}, {"topological", 2}, {"topology", 2}}|>, "1500949" -> <|"AwardTitle" -> "Combinatorics and geometry of mutations", "AwardEffectiveDate" -> DateObject[{2015, 8, 15}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[120000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "The goal of this project is to better understand an operation on matrices called \"mutation.\" A matrix is a collection of numbers arranged in a square grid. Matrix mutation takes a matrix and changes it according to certain rules to make a new matrix. The rules themselves seem strange and counterintuitive, but matrix mutation is happening behind the scenes in many very important mathematical areas, including Teichmüller theory, Poisson geometry, quiver representations, Lie theory, algebraic geometry, algebraic combinatorics, and even partial differential equations (in the equations describing shallow water waves). Matrix mutation appears in certain kinds of algebra (manipulating multivariable functions in a setting called a \"cluster algebra\"), combinatorics (modeling cluster algebras by discrete objects) and geometry (measuring distances in two-dimensional spaces). A key component of this project is to study matrix mutation, with a focus on the \"mutation fan.\" A fan is a way of cutting space into pieces (subject to certain rules). For example, if we draw three different lines through (0,0) in the xy-plane, they cut space into six pieces, and those pieces define a fan. If we take two of the pieces that are right next to each other and glue them together to make one piece, the resulting five pieces are a simple example of a mutation fan. \n\nOne part of the project concerns universal geometric coefficients and mutation fans. Specifically, the goal is to construct the mutation fan for matrices arising from Cartan matrices of affine type and from surfaces, and to construct universal coefficients in those cases. Furthermore, the research will pin down the relationships between mutation fans and other fans, like tropicalized cluster algebras, fans of semi-invariants, and scattering diagrams. A second part of the project concerns the dominance relation on exchange matrices. A matrix B dominates a matrix B' if they have the same (weak) sign pattern and each entry of B is weakly larger than the corresponding entry of B'. The goal of this part of the project is to understand a phenomenon observed in many examples, namely (1) that dominance relations among matrices often lead to refinement relations among mutation fans and (2) that there is often an algebraic relationship between the two cluster algebras. The third part of the project concerns cluster algebras and Coxeter-Catalan combinatorics in affine type. Here the goal is to construct the affine-type analogs of almost-positive root models for cluster algebras, and to relate them to affine doubled Cambrian fans.", "AwardID" -> "1500949", "Institution" -> Entity["NSFInstitution", "NorthCarolinaStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "NathanReading"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500949&HistoricalAwards=false"], "KeywordTally" -> {{"mutation", 11}, {"matrix", 7}, {"cluster", 6}, {"fans", 6}, {"project", 6}, {"algebras", 5}, {"fan", 5}, {"matrices", 5}, {"pieces", 5}, {"B", 4}, {"goal", 4}, {"affine", 3}, {"algebraic", 3}, {"certain", 3}, {"combinatorics", 3}, {"concerns", 3}, {"construct", 3}, {"geometry", 3}, {"rules", 3}, {"algebra", 2}, {"called", 2}, {"coefficients", 2}, {"dominance", 2}, {"entry", 2}, {"equations", 2}, {"example", 2}, {"make", 2}, {"Matrix", 2}, {"relations", 2}, {"space", 2}, {"theory", 2}, {"type", 2}, {"understand", 2}, {"universal", 2}}|>, "1500951" -> <|"AwardTitle" -> "Harmonic Maps between Hyperbolic Spaces, Realizing Number Fields as Invariant Trace Fields, and Constructing Surface Subgroups in Hyperbolic Groups", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[136576, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "Pure mathematics fosters the development of ideas that are later utilized in natural sciences such as physics and biology. In physics, the universe is described as a 3-dimensional space; studying the geometry and topology of 3-manifolds may prove important in answering fundamental physical questions. This project investigates and develops techniques that involve an interplay between coarse hyperbolic geometry and statistical properties of various geometric flows, which are becoming indispensable tools in proving results from a range of fields. Although geometry and dynamics of such flows are not always necessary to state or prove these breakthroughs, they give the 'right' way of thinking about them and are likely to catalyze further progress. Through participation in this research project, the next generation of graduate students will be introduced to these concepts.\n\nThe PI will study questions about geometry of hyperbolic groups and negatively curved manifolds. In connection with the Cannon Conjecture, the question of whether a hyperbolic group whose boundary is the 2-sphere contains an abundance of quasi-convex surface subgroups will be addressed. In a different direction, a Dirichlet type problem of finding harmonic mappings with prescribed quasi-symmetric boundary values will be studied, with particular emphasis on the Schoen Conjecture.", "AwardID" -> "1500951", "Institution" -> Entity["NSFInstitution", "CaliforniaInstituteOfTechnology"], "Investigators" -> {Entity["NSFInvestigator", "VladimirMarkovic"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500951&HistoricalAwards=false"], "KeywordTally" -> {{"geometry", 4}, {"hyperbolic", 3}, {"boundary", 2}, {"Conjecture", 2}, {"flows", 2}, {"physics", 2}, {"project", 2}, {"prove", 2}, {"questions", 2}}|>, "1500952" -> <|"AwardTitle" -> "RUI: Spectral Theory and Geometric Analysis in Several Complex Variables", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[118066, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "Many physical and social phenomena can be modeled mathematically using partial differential operators. The Laplace operator is a differential operator that has long played an important role in mechanics, physics, and mathematics. The complex Laplace operator is a natural outgrowth of the classical Laplace operator in complex analysis of several variables, a branch of mathematics where algebra, analysis, and geometry intertwine. This research project investigates analytic and geometric properties of the complex Laplace operator, in particular, its spectrum. Spectral analysis is a major tool in scientific research, and spectral properties of the complex Laplace operator are known to be closely related to certain quantum phenomena in physics. The goal of this project is to understand how algebraic, analytic, and geometric structures of the underlying complex space interact with each other. The project combines ideas and methods from several branches of mathematics, and the techniques under development could potentially have applications in other areas of mathematics and physical sciences. This project involves undergraduate students in research activities and broadens participation of underrepresented groups in mathematics. \n\nThe complex Neumann Laplace operator is a prototype of an elliptic operator with non-coercive boundary conditions. Since the work of Kohn and Hörmander in the 1960's, there have been extensive studies on regularity theory of the complex Neumann Laplace operator that led to important discoveries in both partial differential equations and several complex variables. The main thrust of this proposal is to study spectral theory of the complex Neumann Laplace operator, with emphasis on the interplay between the spectral behavior of the operator and the underlying geometric structures. Among the problems studied in this project are stability of the spectrum as the underlying structures deform and characterization of complex manifolds whose complex Laplace operator has discrete spectrum. Also investigated are regularity theory of the Cauchy-Riemann operator on complex manifolds, reproducing kernels, invariant metrics, and their applications to problems in complex algebraic geometry. This project supports research activities of undergraduate and graduate students, facilitates the development of new courses that attract students into mathematics, and fosters interdisciplinary research.", "AwardID" -> "1500952", "Institution" -> Entity["NSFInstitution", "RutgersUniversityCamden"], "Investigators" -> {Entity["NSFInvestigator", "SiqiFu"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "9229", "Text" -> "RES IN UNDERGRAD INST-RESEARCH"}, {"Code" -> "9251", "Text" -> "RES EXPER FOR UNDERGRAD-SUPPLT"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500952&HistoricalAwards=false"], "KeywordTally" -> {{"complex", 13}, {"operator", 13}, {"Laplace", 9}, {"mathematics", 6}, {"project", 6}, {"research", 5}, {"analysis", 3}, {"differential", 3}, {"geometric", 3}, {"Neumann", 3}, {"spectral", 3}, {"spectrum", 3}, {"structures", 3}, {"students", 3}, {"theory", 3}, {"underlying", 3}, {"activities", 2}, {"algebraic", 2}, {"analytic", 2}, {"applications", 2}, {"development", 2}, {"geometry", 2}, {"important", 2}, {"manifolds", 2}, {"partial", 2}, {"phenomena", 2}, {"physical", 2}, {"physics", 2}, {"problems", 2}, {"properties", 2}, {"regularity", 2}, {"undergraduate", 2}, {"variables", 2}}|>, "1500954" -> <|"AwardTitle" -> "Lefschetz Fibrations, Mapping Tori, and Dynamics on Moduli Spaces of Objects", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[206807, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Joanna Kania-Bartoszynska", "Abstract" -> "Dynamical systems (mathematical models of systems changing in time) describe many processes that affect us, and have given rise to some of the hardest questions in science, such as the multi-body problem in celestial mechanics. The first part of this project aims to explore an entirely new kind of dynamics, in which the states of the system (such as positions of particles) move around in time, without a global motion of the entire system. This seems paradoxical, and indeed one expects it to happen mostly in situations that are far from applications. Nevertheless, it has been shown that the phenomenon is mathematically possible, and because dynamical systems thinking provides such a powerful intuition, it makes sense to want to stretch its limits as far as possible. Any evidence of additional complexity in classical mechanical systems, even if it directly affects only a few cases, ultimately changes how we think of the complexity of such systems in general. The second part of this project deals with a phenomenon in mathematics which arises from its current close exchange of ideas with string theory: namely, the appearance of complicated explicit functions (typically, of one variable). From the viewpoint of topology, which is more qualitative, one hopes to minimize the amount of information that needs to be encoded inside such functions. For instance, if the functions themselves solve a differential equation, they can be recovered from a finite amount of information. String theory has been very effective in providing such a characterization, but this project aims (in a special case) for a more direct and simpler description. It should be viewed as an exercise in \"noncommutative geometry\", which is the mathematicians' way to prepare ourselves for thinking beyond conventional notions of space (which is one of the big challenges in contemporary mathematics and physics).\n\nSymplectic manifolds have a rich internal structure. This can be approached from a variational viewpoint (capacities, Hofer norms, spectral invariants), or from string theory and mirror symmetry. Nevertheless, the basic known invariants are a collection of numbers, or homology classes (Gromov-Witten invariants). There is information beyond that (Lagrangian submanifolds, Fukaya categories), but it is not directly amenable to being used as a classification tool. The project intends to attack this situation by looking at dynamical systems acting on the Fukaya category. The idea is start with geometric considerations such as flux, and export them to other situations. The approach is designed to be applied to a specific class of symplectic manifolds, related to mapping tori. The other major topic is a way of computing Fukaya categories, using Lefschetz pencils. While there is a body of previous work in this direction, it is restricted to the exact (or monotone) situation, and does not address the challenge of understanding the infinite series that arise in the Calabi-Yau case. The PI's aim is to describe those series in a more direct way than is provided by the standard framework of mirror symmetry (Gauss-Manin connections, mirror maps); this description would then also be more general, since it is ultimately independent of mirror symmetry considerations.", "AwardID" -> "1500954", "Institution" -> Entity["NSFInstitution", "MassachusettsInstituteOfTechnology"], "Investigators" -> {Entity["NSFInvestigator", "PaulSeidel"]}, "ProgramElements" -> {{"Code" -> "1267", "Text" -> "TOPOLOGY"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500954&HistoricalAwards=false"], "KeywordTally" -> {{"systems", 6}, {"mirror", 4}, {"project", 4}, {"Fukaya", 3}, {"functions", 3}, {"information", 3}, {"invariants", 3}, {"symmetry", 3}, {"theory", 3}, {"way", 3}, {"aims", 2}, {"amount", 2}, {"beyond", 2}, {"case", 2}, {"categories", 2}, {"complexity", 2}, {"considerations", 2}, {"describe", 2}, {"description", 2}, {"direct", 2}, {"directly", 2}, {"dynamical", 2}, {"far", 2}, {"general", 2}, {"manifolds", 2}, {"mathematics", 2}, {"Nevertheless", 2}, {"phenomenon", 2}, {"possible", 2}, {"series", 2}, {"situation", 2}, {"situations", 2}, {"string", 2}, {"system", 2}, {"thinking", 2}, {"time", 2}, {"ultimately", 2}, {"viewpoint", 2}}|>, "1500958" -> <|"AwardTitle" -> "Topics in Harmonic Analysis: Interplay between Time-Frequency Analysis, Additive Combinatorics and Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[179537, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This research project focuses on the interplay between three major areas in mathematics: harmonic analysis, additive combinatorics, and partial differential equations (PDE), with the harmonic analysis component playing the dominant role. The research plan has the following characteristics: (1) it is structured into several classes of problems (some to be detailed in the next paragraph), on some of which the principal investigator has already made relevant contribution/advancements by developing new analysis methods; (2) it covers a wide range of techniques, with levels of difficulty varying depending on the nature of the subject that also allow partial progress; (3) it has two main components, namely, a purely theoretical one dealing with problems that focus on understanding the behavior of various so-called maximal operators with highly oscillatory kernels and a more applied side, part of the area of fluid dynamics, studying the problem of singularity formation for two-fluid interfaces. An advancement in this latter direction will contribute to a better understanding of the physical reality around us. Further aspects of the project are the dissemination of the principal investigator's work through conference participation, lectures, and graduate courses, interaction with other researchers/experts in the areas of harmonic analysis and PDE, the training of graduate students and postdoctoral fellows. \n\nThis project investigates several problems that position themselves at the interface either between harmonic analysis and additive combinatorics, or between harmonic analysis and fluid dynamics. It is structured along several major themes, among which we mention the following (items (2), (3), and (4) represent joint projects with collaborators): (1) pointwise convergence of Fourier series near L^1; (2) the maximal Schrodinger operator, Kakeya extremizers, and sum-product estimates; (3) formation of singularities for the two-dimensional, two-fluid interface in the absence of vorticity in order to increase understanding of the \"limiting\" water-wave case; (4) the rotational two-dimensional water-wave problem and quasilinear systems of Klein--Gordon equations in three dimensions with nontrivial vorticity, with a focus on the time of existence for small initial data. On the first topic the author has already made contributions, developing new methods that either improved on known results (e.g., the pointwise convergence along lacunary subsequences of partial Fourier sums) or recovered the best known results stemming from the celebrated work of Lennart Carleson. The approaches for both the first and second topics combine techniques from time-frequency analysis and additive combinatorics. The third theme investigates, for the two-dimensional, two-fluid problem, how the geometry of the interface changes as the boundary approaches a \"splash\" scenario from the water-wave case; the fourth one explores how the time of existence for solutions (relative to small initial data) of the two-dimensional water-wave case and three dimensional Klein-Gordon systems are affected by the presence of vorticity, a new and hitherto mostly unexplored theme in the fluid dynamics literature.", "AwardID" -> "1500958", "Institution" -> Entity["NSFInstitution", "PurdueUniversity"], "Investigators" -> {Entity["NSFInvestigator", "VictorLie"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500958&HistoricalAwards=false"], "KeywordTally" -> {{"analysis", 7}, {"harmonic", 5}, {"-dimensional", 4}, {"water-wave", 4}, {"additive", 3}, {"case", 3}, {"combinatorics", 3}, {"dynamics", 3}, {"-fluid", 3}, {"fluid", 3}, {"interface", 3}, {"new", 3}, {"partial", 3}, {"problem", 3}, {"problems", 3}, {"project", 3}, {"understanding", 3}, {"vorticity", 3}, {"1", 2}, {"2", 2}, {"3", 2}, {"4", 2}, {"approaches", 2}, {"areas", 2}, {"convergence", 2}, {"data", 2}, {"developing", 2}, {"equations", 2}, {"existence", 2}, {"focus", 2}, {"following", 2}, {"formation", 2}, {"Fourier", 2}, {"graduate", 2}, {"initial", 2}, {"investigates", 2}, {"known", 2}, {"major", 2}, {"maximal", 2}, {"methods", 2}, {"PDE", 2}, {"pointwise", 2}, {"principal", 2}, {"research", 2}, {"results", 2}, {"small", 2}, {"structured", 2}, {"systems", 2}, {"techniques", 2}, {"theme", 2}, {"time", 2}, {"work", 2}}|>, "1500963" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Evolution of Angiosperm Seed Development: perspectives from Nymphaea thermarum (Nymphaeales)", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2017, 5, 31}], "AwardAmount" -> Quantity[21772, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010207", "ProgramOfficer" -> "Leslie Rissler", "Abstract" -> "Seeds of flowering plants are distinguished by the presence of a novel tissue - endosperm. Endosperm is the product of a second fertilization event, but rather than developing into a second embryo, it becomes a tissue that mediates the relationship between the maternal plant and its compatriot embryo. Endosperm is also an essential part of the human diet: the seeds that provide most of the calories people consume (rice, wheat, corn) consist primarily of endosperm. Studies in model plant species have begun to piece together the mechanisms that control endosperm development, and have revealed that gene imprinting plays an important role. Imprinting occurs when an allele inherited from one parent is silenced. Little scientific attention has been given to how imprinting has evolved in flowering plants. This project will address this discrepancy by analyzing the expression of genes during development of endosperm in the water lily, which is a member of one of the most ancient lineages of flowering plants. While the water lily is uniquely suited to become a model system for the early diverging lineages, it is also on the brink of extinction - making it a compelling case for why exploring and preserving biodiversity is essential for furthering basic scientific research.\n\nAnalysis of gene expression will be accomplished by creating RNA-seq transcriptomes of key stages during ovule and seed development. From this dataset, two main categories of genes will be targeted for homolog identification: genes that are involved in imprinting-regulation mechanisms and genes that are themselves imprinted. Simple presence/absence of homologs of these genes during seed development in N. thermarum will help to resolve the question of when during angiosperm evolution did these mechanisms became important regulators of endosperm development. In addition, the sampling scheme will make it possible to distinguish suites of gene activity that correlate to specific sets of developmental processes. Finally, the accompanying sequence and expression data will be used to reconstruct the evolutionary history of relevant gene families. This database will represent an important resource for understanding the evolution of angiosperm seeds, and will be made publically available.", "AwardID" -> "1500963", "Institution" -> Entity["NSFInstitution", "HarvardUniversity"], "Investigators" -> {Entity["NSFInvestigator", "WilliamFriedman"], Entity["NSFInvestigator", "RebeccaPovilus"]}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500963&HistoricalAwards=false"], "KeywordTally" -> {{"development", 5}, {"endosperm", 5}, {"genes", 5}, {"gene", 4}, {"expression", 3}, {"flowering", 3}, {"important", 3}, {"mechanisms", 3}, {"plants", 3}, {"angiosperm", 2}, {"embryo", 2}, {"Endosperm", 2}, {"essential", 2}, {"evolution", 2}, {"imprinting", 2}, {"lily", 2}, {"lineages", 2}, {"model", 2}, {"plant", 2}, {"presence", 2}, {"scientific", 2}, {"second", 2}, {"seed", 2}, {"seeds", 2}, {"tissue", 2}, {"water", 2}}|>, "1500965" -> <|"AwardTitle" -> "Renormalization in piecewise isometric dynamical systems", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[115340, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce Kitchens", "Abstract" -> "A collection of objects whose changes are governed by a time-independent update rule is called a dynamical system. Examples are pervasive in the sciences, including the motion of celestial bodies, weather patterns, the behavior of fluids moving through a pipe, and chemical processes. A basic question in the subject is to determine the behavior of such a system. So called hyperbolic dynamical systems are a prime example of success in the field. These systems admit a special kind of expansion and contraction, which make available certain mathematical methods of analyzing the behavior of these systems. This project centers on understanding systems at the opposite extreme, piecewise isometric systems, which admit no contraction or expansion and thus force different approaches to be used to understand these systems. These systems are typically understood through renormalization. Renormalization is a method of looking more and more closely at, or zooming in on, repeated behavior. Renormalization is a major part of this project and the PI will develop new renormalization methods and improve existing methods to understand these systems. A better understanding of these systems will have broad consequences for our understanding of dynamical systems as a subject. In addition to the research aims of the project, the PI will work with students, providing mentoring and training in mathematical research.\n\nThe PI will make contributions toward the use of renormalization to understand dynamical phenomena in piecewise isometric dynamical systems and related systems. Systems of interest include horocyclic flows on hyperbolic surfaces, geodesic flows on flat manifolds, and piecewise isometric systems. Many of these systems arise naturally through connections with low-dimensional topology and geometry. A piecewise isometry is formed by cutting a metric space into pieces and applying an isometry to each piece so as to reassemble the whole space. Examples include interval exchange transformations (IETs), where the space is an interval, which is cut into finitely many subintervals. The theory of IETs is quite well developed and stands as a testament to the power of renormalization methods, but in contrast, many related systems are only poorly understood. A primary goal is to extend the applicability of renormalization methods to wider classes of systems including polygon exchange transformations, and infinite interval exchange transformations. New dynamical phenomena will be discovered and rigorously studied using the renormalization methods developed by the PI. Results produced by research in this proposal will widely disseminated through publication in research journals and through conference presentations.", "AwardID" -> "1500965", "Institution" -> Entity["NSFInstitution", "CUNYCityCollege"], "Investigators" -> {Entity["NSFInvestigator", "WilliamHooper"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500965&HistoricalAwards=false"], "KeywordTally" -> {{"systems", 16}, {"dynamical", 6}, {"methods", 6}, {"renormalization", 6}, {"behavior", 4}, {"PI", 4}, {"piecewise", 4}, {"exchange", 3}, {"interval", 3}, {"isometric", 3}, {"project", 3}, {"research", 3}, {"space", 3}, {"transformations", 3}, {"understand", 3}, {"understanding", 3}, {"admit", 2}, {"called", 2}, {"contraction", 2}, {"developed", 2}, {"Examples", 2}, {"expansion", 2}, {"flows", 2}, {"hyperbolic", 2}, {"IETs", 2}, {"include", 2}, {"including", 2}, {"isometry", 2}, {"make", 2}, {"mathematical", 2}, {"phenomena", 2}, {"related", 2}, {"Renormalization", 2}, {"subject", 2}, {"system", 2}, {"understood", 2}}|>, "1500966" -> <|"AwardTitle" -> "Enumeration Problems in Algebraic Geometry and Representation Theory", "AwardEffectiveDate" -> DateObject[{2015, 9, 15}], "AwardExpirationDate" -> DateObject[{2017, 8, 31}], "AwardAmount" -> Quantity[100000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This research project concerns both algebraic geometry, which seeks to characterize solutions to algebraic equations with geometry, and representation theory, which is a systematic investigation of symmetry. Despite their abstract nature, the answers to many questions in both of these subjects boil down to being able to compute certain numbers. The purpose of this research project is to use new techniques from algebraic geometry and commutative algebra to recast these numbers as combinatorial quantities, making them easier to understand with a computer. By utilizing conceptual connections to other scientific fields, this research will also advance the understanding of several questions in mathematical physics and mathematical biology. Undergraduate students are involved directly as collaborators in the project, providing them with training in advanced mathematical topics and the use of 3D printing techniques in mathematical research.\n\nThe algebraic geometry of moduli spaces of principal bundles and branching varieties naturally produces two interesting enumeration problems: counting branching multiplicities of a map of reductive groups, and finding the dimension of the spaces of conformal blocks from the Wess-Zumino-Novikov-Witten model of conformal field theory. This research aims to further understanding of these quantities using the theory of Newton-Okounkov bodies and the quickly evolving field of Berkovich geometry. These theories will be used to provide new polyhedral descriptions of conformal blocks and branching multiplicities, as well as further the understanding of the topology and symplectic geometry of the spaces under consideration.", "AwardID" -> "1500966", "Institution" -> Entity["NSFInstitution", "GeorgeMasonUniversity"], "Investigators" -> {Entity["NSFInvestigator", "ChristopherManon"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500966&HistoricalAwards=false"], "KeywordTally" -> {{"geometry", 6}, {"algebraic", 4}, {"mathematical", 4}, {"research", 4}, {"branching", 3}, {"conformal", 3}, {"project", 3}, {"spaces", 3}, {"theory", 3}, {"understanding", 3}, {"blocks", 2}, {"field", 2}, {"multiplicities", 2}, {"new", 2}, {"numbers", 2}, {"quantities", 2}, {"questions", 2}, {"techniques", 2}, {"use", 2}}|>, "1500974" -> <|"AwardTitle" -> "Descriptive set theory and recursion theory", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[55130, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "A fundamental problem encountered throughout mathematics is to completely classify some type of mathematical object by invariants. Descriptive set theory gives a general framework for studying such classification problems and comparing their relative difficulties. The field has had remarkable success, proving the existence of barriers to having simple types of classifications, calibrating the difficulty of classification problems in a variety of fields of mathematics, and in understanding the structure of the space of all classification problems. This study has had particularly close connections with ergodic theory, probability, and operator algebras.\n\nThis project studies the difficulty of classifying countable Borel equivalence relations using new techniques based on Borel determinacy and recursion theory. These tools have already resolved several important questions in the field, and are promising candidates for attacking problems in the subject which are known to require new methods, such as the increasing unions problem for hyperfinite equivalence relations, and the question of whether Turing equivalence is universal. This work is also closely connected to the study of descriptive graph combinatorics. Recent breakthroughs in this area have yielded new combinatorial methods for studying problems in the field of countable Borel equivalence relations, and these connections have also inspired new combinatorial investigations.", "AwardID" -> "1500974", "Institution" -> Entity["NSFInstitution", "UniversityOfCalifornia-LosAngeles"], "Investigators" -> {Entity["NSFInvestigator", "AndrewMarks"]}, "ProgramElements" -> {{"Code" -> "1268", "Text" -> "FOUNDATIONS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500974&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 5}, {"equivalence", 4}, {"new", 4}, {"Borel", 3}, {"classification", 3}, {"field", 3}, {"relations", 3}, {"theory", 3}, {"combinatorial", 2}, {"connections", 2}, {"countable", 2}, {"difficulty", 2}, {"mathematics", 2}, {"methods", 2}, {"problem", 2}, {"study", 2}, {"studying", 2}}|>, "1500976" -> <|"AwardTitle" -> "Model Theory and Difference Algebra", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[103389, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "Logic is the study of formal reasoning rules that rely on the grammatical structure of the statements rather than their content. Revived in the beginning of the twentieth century to deal with some foundational issues, mathematical logic turned out to also be useful for obtaining new results in mathematics. The recent applications of the model theory of difference and differential algebra to algebraic number theory are some of the most exciting examples of this. Difference equations, like differential equations, model real-world processes that change over time. Differential equations describe quantities that vary continuously with time, such as the positions of planets in space, while difference equations describe quantities that are only measured at discrete time intervals, such as the annual GDP of a country. Difference algebra is the abstract setting for studying difference equations; it also has applications to the kind of algebraic number theory that underpins modern cryptography and internet security. Medvedev proposes to study the fine structure of solution sets of difference equations: to find algorithms for computing their dimensions and for identifying the very special cases where it is possible to define some kind of addition and/or multiplication on these sets.\n\nA difference field is a field with a distinguished automorphism. The theory of difference closed fields is supersimple, meaning that Lascar rank is a good notion of dimension for complete types. Furthermore, the complete types of Lascar rank 1 satisfy the Zilber Trichotomy: each is nonorthogonal to a definable field, or nonorthogonal to a definable one-based group, or is disintegrated. While the fieldlike case of the trichotomy is relatively easy to identify in explicit examples, the dividing line between the grouplike and the disintegrated cases is much less clear. Similarly, even in the relatively nice case of groups, it is not always easy to determine the Lascar rank of a particular type. Beginning with her PhD thesis, Medvedev has worked on these sorts of problems, and on applications to algebraic dynamics. She is confident that she can generalize the main theorem of her PhD thesis from curves to higher-dimensional algebraic varieties. She has already accomplished the first part of this in far greater generality; the last part of the original proof should generalize easily; and the middle piece is supplied by an observation in a paper by Chatzidakis and Hrushovski. She expects to also obtain concrete results on the Lascar rank of certain groups G defined by systems of polynomial difference equations. This question can be translated to the language of linear algebra over the quasiendomorphism ring of the underlying algebraic group. For example, when G is a subgroup of the multiplicative group of a field in characteristic zero, this question reduces to linear algebra over the field of rational numbers. In addition, Medvedev proposes to continue expanding her foundational notes about difference schemes defined by Hrushovski in his work on the model theory of Frobenius automorphisms, filling in many missing detail, adding enlightening examples, and reorganizing the presentation to make it (more) understandable. Medvedev expects to continue involving students in this work, encouraging logicians and algebraic geometers to learn each other's languages when they are still young.", "AwardID" -> "1500976", "Institution" -> Entity["NSFInstitution", "CUNYCityCollege"], "Investigators" -> {Entity["NSFInvestigator", "AliceMedvedev"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500976&HistoricalAwards=false"], "KeywordTally" -> {{"difference", 8}, {"equations", 7}, {"algebraic", 6}, {"field", 5}, {"theory", 5}, {"algebra", 4}, {"Lascar", 4}, {"Medvedev", 4}, {"rank", 4}, {"applications", 3}, {"examples", 3}, {"group", 3}, {"model", 3}, {"time", 3}, {"addition", 2}, {"case", 2}, {"cases", 2}, {"complete", 2}, {"continue", 2}, {"definable", 2}, {"defined", 2}, {"describe", 2}, {"Difference", 2}, {"differential", 2}, {"disintegrated", 2}, {"easy", 2}, {"expects", 2}, {"foundational", 2}, {"G", 2}, {"generalize", 2}, {"groups", 2}, {"Hrushovski", 2}, {"kind", 2}, {"linear", 2}, {"nonorthogonal", 2}, {"number", 2}, {"PhD", 2}, {"proposes", 2}, {"quantities", 2}, {"question", 2}, {"relatively", 2}, {"results", 2}, {"structure", 2}, {"study", 2}, {"thesis", 2}, {"types", 2}, {"work", 2}}|>, "1500977" -> <|"AwardTitle" -> "Topics in Automorphic Forms", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2018, 6, 30}], "AwardAmount" -> Quantity[134400, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "Fourier analysis implies that functions that are periodic -- for example, quantities depending on time that repeat their previous value a fixed amount of time later -- can be realized as sums of trigonometric functions. Functions with more complicated, non-commutative, periodicities are at the heart of modern number theory. A fundamental vision of Langlands predicts connections between such functions and symmetries related to arithmetic, that is, coming from roots of polynomial equations. This proposal is concerned with periodic functions in a new guise, when the functions are defined not on a group but on a finite cover of a group. This blends arithmetic and analysis in a new way. Moreover, the techniques to be studied may have connections to constructions in mathematical physics.\n\nThe main objects of study in this project are automorphic forms on covering groups. The principal investigator will focus first on Eisenstein series, which are obtained by an averaging process. Many of the standard tools from automorphic forms do not carry over (e.g. Whittaker functionals are typically not unique), but a surprising picture blending representation theory (canonical bases, Mirkovi\\'c-Vilonen cycles) and number theory is emerging. The principal investigator will investigate these and and their number-theoretic applications. He also will study the residues of metaplectic Eisenstein series, \"higher theta series.\" There is much to be done to understand the unipotent orbits attached to these objects, to develop relations between such series on different groups, and to use them both globally and in local constructions. A third project concerns unique functionals and Iwahori Hecke algebras. It offers the potential for new constructions of unique functionals.", "AwardID" -> "1500977", "Institution" -> Entity["NSFInstitution", "BostonCollege"], "Investigators" -> {Entity["NSFInvestigator", "SolomonFriedberg"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500977&HistoricalAwards=false"], "KeywordTally" -> {{"functions", 5}, {"series", 4}, {"constructions", 3}, {"functionals", 3}, {"new", 3}, {"theory", 3}, {"unique", 3}, {"analysis", 2}, {"arithmetic", 2}, {"automorphic", 2}, {"connections", 2}, {"Eisenstein", 2}, {"forms", 2}, {"group", 2}, {"groups", 2}, {"investigator", 2}, {"number", 2}, {"objects", 2}, {"periodic", 2}, {"principal", 2}, {"project", 2}, {"study", 2}, {"time", 2}}|>, "1500982" -> <|"AwardTitle" -> "Workshop Travel to Study Analysis and Geometry in Metric Spaces", "AwardEffectiveDate" -> DateObject[{2015, 5, 1}], "AwardExpirationDate" -> DateObject[{2016, 10, 31}], "AwardAmount" -> Quantity[47840, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "This award will provide support for sixteen U.S. mathematicians to participate in the Research Term on Analysis and Geometry in Metric Spaces from April through June, 2015 at the Instituto de Ciencias Matemáticas (ICMAT) in Madrid, Spain. Metric spaces are useful models anytime one wants to consider sets of objects with a natural notion of \"distance\" -- for example, images, DNA sequences, and data in general can be modeled with metric spaces. Developing calculus in metric spaces is useful in part because it allows one to formulate and solve optimization problems in these settings. This research term will, in particular, integrate metric space theory with a wide variety of applications including image processing, reconstruction theory, control theory, and robotics.\n\nMore specifically, program brings together three areas of metric space research: first-order analysis (including theories of Sobolev spaces, solutions to the p-Laplace equation, and functions of bounded variation on metric measure spaces), geometric measure theory and variational problems (particularly in the sub-Riemannian setting), and versions of weak curvature (for example, the the setting of Alexandrov spaces). It is expected to facilitate crossflow of ideas and techniques between these areas and establish international collaborations between researchers. The schedule includes four, week-long minicourses for non-specialists and young researchers during the month of May taught by leading experts in metric space analysis and geometry, followed by a workshop in June that brings together topics from the minicourses. Priority for travel support from this award will be given to graduate students, early-career mathematicians, and mathematicians from under-represented groups.\n\nResearch Term web site: http://www.icmat.es/RT/AGMS2015/", "AwardID" -> "1500982", "Institution" -> Entity["NSFInstitution", "KenyonCollege"], "Investigators" -> {Entity["NSFInvestigator", "MarieSnipes"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500982&HistoricalAwards=false"], "KeywordTally" -> {{"metric", 6}, {"spaces", 6}, {"theory", 4}, {"mathematicians", 3}, {"space", 3}, {"analysis", 2}, {"areas", 2}, {"award", 2}, {"brings", 2}, {"example", 2}, {"including", 2}, {"June", 2}, {"measure", 2}, {"Metric", 2}, {"minicourses", 2}, {"problems", 2}, {"research", 2}, {"researchers", 2}, {"setting", 2}, {"support", 2}, {"Term", 2}, {"useful", 2}}|>, "1500984" -> <|"AwardTitle" -> "Direct and Inverse Problems for Cardinality Questions in Additive Combinatorics", "AwardEffectiveDate" -> DateObject[{2015, 10, 1}], "AwardExpirationDate" -> DateObject[{2018, 9, 30}], "AwardAmount" -> Quantity[36062, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "Combinatorics is arguably the most accessible branch of pure mathematics. At its core lie elementary questions that might excite a high school student as much as an expert. For example, imagine that one colors the edges and diagonals of an icosahedron red or blue. Can one always find a triangle whose edges are all red or a triangle whose edges are all blue? While combinatorics has traditionally found applications in computer science, information theory, and mathematical models, this project aims to further investigate its applications to what must be the oldest part of mathematics: number theory. The PI will involve high school, undergraduate, and graduate students in the project. The problems under study are suitable for training in research as they are easily accessible and offer an excellent setting for grasping some of the core techniques used in combinatorics. Parallel to and supported by the research activities of the project, the PI's goal is to write a short book on the application of combinatorics to number theory aimed at undergraduates in mathematics. \n\nInverse theorems have catalyzed the development of additive combinatorics in recent years. However, some very basic inverse questions remain largely untouched. This project focuses on the study of open questions where combinatorial methods are likely to be of use. Three indicative examples, which are easy to formulate and hence will reach a wide mathematical audience, are: what structural information can be derived for finite sets in a commutative group that have near maximum number of h-fold sums; what can be said about finite sets of integers whose exponential sum has nearly minimum norm; and what can be deduced about the number of distinct differences that are formed from pairs of elements of a finite set, when the number of distinct sums is known? It is hoped that a combination of recent advances in the field and novel ideas will lead to progress. As these questions are representative of the challenges one must overcome in a wider variety of cardinality questions in additive combinatorics. It is hoped that any discoveries will be applied to other contexts as well. The project's methodology has a strong interdisciplinary component, which could unearth new connections between combinatorics and harmonic analysis.", "AwardID" -> "1500984", "Institution" -> Entity["NSFInstitution", "UniversityOfRochester"], "Investigators" -> {Entity["NSFInvestigator", "GeorgiosPetridis"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500984&HistoricalAwards=false"], "KeywordTally" -> {{"combinatorics", 6}, {"number", 5}, {"questions", 5}, {"project", 4}, {"edges", 3}, {"finite", 3}, {"mathematics", 3}, {"theory", 3}, {"accessible", 2}, {"additive", 2}, {"applications", 2}, {"blue", 2}, {"core", 2}, {"distinct", 2}, {"high", 2}, {"hoped", 2}, {"information", 2}, {"mathematical", 2}, {"recent", 2}, {"red", 2}, {"research", 2}, {"school", 2}, {"sets", 2}, {"study", 2}, {"sums", 2}, {"triangle", 2}}|>, "1500987" -> <|"AwardTitle" -> "Topological and algebraic combinatorics of posets and stratified spaces", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[140000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This research project is in discrete mathematics, namely, the area of mathematics which provides the theoretical underpinnings for computer science as well as more recently for some substantial parts of biology. The PI particularly focuses on developing novel ways of combining geometric and topological techniques and intuition with combinatorial methods. In recent years, the PI has become particularly focused on finding effective ways to study topological-combinatorial structures on spaces of real-valued matrices satisfying naturally arising constraints, for instance matrices in which the determinant as well as all minors are nonnegative. Such spaces arise both in areas of theoretical mathematics such as representation theory and also in applications areas. For instance, they play an important role to our understanding of the relationship between current and voltage in electrical networks. The more theoretical results can sometimes give surprisingly powerful insights into such applications. The project also includes a study of how configurations of distinct points may move around in space without bumping into each other, taking an abstract, representation theoretic perspective. The PI will also continue her work in helping develop the STEM pipeline both through the training of graduate students in combinatorics and also through organizing workshops and other activities to help inspire and foster the development of the next generation of scientists.\n\nThe specific projects include: (1) analysis of the homeomorphism type of fibers of maps to totally nonnegative varieties; (2) stability properties for configuration spaces related to the partition lattice via a mixture of poset topology and symmetric function theory; (3) analysis of combinatorial topological structure on spaces of electrical networks; and (4) development of poset-theoretic approaches to polytope diameter bounds for particularly nice classes of polytopes, motivated by complexity questions from operations research regarding linear programming. Many of these projects are collaborative. This work builds upon the PI's past research in topological combinatorics, and particularly in poset topology and in combining ideas of geometric topology with those of combinatorics to study combinatorial topological structure of stratified spaces.", "AwardID" -> "1500987", "Institution" -> Entity["NSFInstitution", "NorthCarolinaStateUniversity"], "Investigators" -> {Entity["NSFInvestigator", "PatriciaHersh"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500987&HistoricalAwards=false"], "KeywordTally" -> {{"spaces", 5}, {"particularly", 4}, {"topological", 4}, {"combinatorial", 3}, {"combinatorics", 3}, {"mathematics", 3}, {"PI", 3}, {"research", 3}, {"study", 3}, {"theoretical", 3}, {"topology", 3}, {"analysis", 2}, {"applications", 2}, {"areas", 2}, {"combining", 2}, {"development", 2}, {"electrical", 2}, {"geometric", 2}, {"instance", 2}, {"matrices", 2}, {"networks", 2}, {"nonnegative", 2}, {"poset", 2}, {"project", 2}, {"projects", 2}, {"representation", 2}, {"structure", 2}, {"theory", 2}, {"ways", 2}, {"work", 2}}|>, "1500991" -> <|"AwardTitle" -> "Twenty-Eighth Cumberland Conference on Combinatorics, Graph Theory, and Computing", "AwardEffectiveDate" -> DateObject[{2015, 3, 1}], "AwardExpirationDate" -> DateObject[{2016, 2, 29}], "AwardAmount" -> Quantity[15000, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "The 28th Cumberland Conference on Combinatorics, Graph Theory, and Computing will be held at the Columbia Campus of the University of South Carolina, May 15-17, 2015 (see the conference web site: http://imi.cas.sc.edu/events/cumberland/). This is the twenty-eighth in a sequence of annual conferences that bring together students and researchers from across the Southeastern region to discuss the latest progress in discrete mathematics and computer science. Four featured speakers of international standing will give one hour plenary presentations covering significant advances in discrete mathematics. Estimated attendance is around 100 participants; about forty contributed talks of length 20--25 minutes are planned. The Cumberland Conference series features talks by leading experts, promotes applications of discrete mathematics (particularly in computer science), provides settings that are conducive to collaboration, and supports students and groups underrepresented in mathematics. The conference series has developed a unique role as a regional exchange for researchers at all levels, providing an accessible forum for junior faculty and students to present their work. This award supports the participation of the four principal speakers, of other participants without federal support, and of students and attendees from underrepresented groups.\n\nDiscrete mathematics is a rapidly developing and expanding field of mathematics due to the fact that discrete models are appropriate for a great number of phenomena in communication, network and information science, life sciences, and engineering. The number of researchers and the number of universities offering courses in discrete mathematics is steadily increasing, and so does number of graduate students and undergraduate research students in this field. The Cumberland Conference has established a unique role as a regional forum open to a wide group of students and researchers in discrete mathematics and computer science. This conference plays a significant part in the professional development of graduate students and recent Ph.D.'s, for whom this conference provides an opportunity to present their work, learn of recent advances, form collaborations, and do networking. This year's conference will continue this tradition. Four internationally-known featured speakers will attract a wide audience, while researchers from around the region will present high quality talks. The conference will cover diverse areas in combinatorics, graph theory, and areas overlapping with computer science. This is the first time that the Cumberland Conference will be hosted in South Carolina. It provides an important opportunity to graduate students in South Carolina and nearby to attend a major conference in discrete mathematics.", "AwardID" -> "1500991", "Institution" -> Entity["NSFInstitution", "UniversityOfSouthCarolinaAtColumbia"], "Investigators" -> {Entity["NSFInvestigator", "LinyuanLu"], Entity["NSFInvestigator", "EvaCzabarka"]}, "ProgramElements" -> {{"Code" -> "7970", "Text" -> "Combinatorics"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}, {"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500991&HistoricalAwards=false"], "KeywordTally" -> {{"mathematics", 9}, {"students", 9}, {"conference", 7}, {"discrete", 7}, {"researchers", 5}, {"science", 5}, {"computer", 4}, {"Conference", 4}, {"Cumberland", 4}, {"number", 4}, {"Carolina", 3}, {"graduate", 3}, {"present", 3}, {"provides", 3}, {"South", 3}, {"speakers", 3}, {"talks", 3}, {"advances", 2}, {"areas", 2}, {"featured", 2}, {"field", 2}, {"forum", 2}, {"opportunity", 2}, {"participants", 2}, {"recent", 2}, {"region", 2}, {"regional", 2}, {"role", 2}, {"series", 2}, {"significant", 2}, {"supports", 2}, {"underrepresented", 2}, {"unique", 2}, {"wide", 2}, {"work", 2}}|>, "1500997" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: Highly unsaturated fatty acid transfer from aquatic to terrestrial food webs", "AwardEffectiveDate" -> DateObject[{2015, 7, 1}], "AwardExpirationDate" -> DateObject[{2017, 6, 30}], "AwardAmount" -> Quantity[20151, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010209", "ProgramOfficer" -> "Matthew Kane", "Abstract" -> "Streams depend upon nutrients from terrestrial landscapes to fuel the production of the plants and animals living in them. Reciprocally, stream organisms such as emerging aquatic insects provide energy and nutrients to terrestrial predators, including streamside birds. Emergent stream insects are likely an especially important food source for streamside predators. Most past studies on nutrient movement between streams and terrestrial landscapes have been conducted in relatively undisturbed forests. However, the contribution of stream-derived nutrients to streamside predators may actually be less important in forested streams than in highly productive streams in agricultural landscapes where algae and stream insects are abundant. This research will examine effects of: 1) food availability and quality on the growth rates of a representative streamside bird, the Eastern Phoebe (Sayornis phoebe), and 2) agricultural versus forested land use on the availability and quality of freshwater and terrestrial food resources for Eastern Phoebe chicks. The researchers will collaborate with local environmental managers and landowners by sharing summaries of results, and at publicly accessible study sites, informational signs will be used to explain the research. The researchers will work with a local children's science museum to develop presentations based on the research themes, and will continue to mentor underrepresented minority undergraduates.\n\nEffects of food quality and quantity will be measured by raising phoebe chicks during their most rapid period of growth (days 4-9) in lab settings. Chicks will be fed diets that vary in quantity (high or low calorie) and quality (high or low highly unsaturated fatty acids) in a two by two design. Phoebe chick weight, head length, and tarsus length will be measured daily. To examine the effects of land use on food quality and quality in a natural setting, chick growth measurements will be coupled to fatty acid composition analyses to quantify food quality across sites. Stable isotope analyses of phoebe tissues and their terrestrial and aquatic dietary items will be used to reconstruct where phoebes obtain food resources. The researchers expect agricultural sites to provide phoebes with both higher food quantity and quality resulting in faster phoebe growth rates. Compound-specific stable isotope analyses of phoebe tissues and their terrestrial and aquatic dietary items will be performed to determine how land use affects where phoebes obtain highly unsaturated fatty acids. The researchers expect phoebes at agricultural sites to obtain highly unsaturated fatty acids synthesized by aquatic primary producers and phoebes at forested sites to obtain highly unsaturated fatty acids elongated from their molecular precursors synthesized by terrestrial primary producers.", "AwardID" -> "1500997", "Institution" -> Entity["NSFInstitution", "CornellUniversity"], "Investigators" -> {Entity["NSFInvestigator", "AlexanderFlecker"], Entity["NSFInvestigator", "CorneliaTwining"]}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500997&HistoricalAwards=false"], "KeywordTally" -> {{"food", 8}, {"quality", 8}, {"terrestrial", 7}, {"fatty", 5}, {"highly", 5}, {"phoebe", 5}, {"phoebes", 5}, {"sites", 5}, {"acids", 4}, {"agricultural", 4}, {"aquatic", 4}, {"growth", 4}, {"obtain", 4}, {"researchers", 4}, {"streamside", 4}, {"unsaturated", 4}, {"analyses", 3}, {"forested", 3}, {"insects", 3}, {"land", 3}, {"landscapes", 3}, {"nutrients", 3}, {"Phoebe", 3}, {"predators", 3}, {"quantity", 3}, {"research", 3}, {"stream", 3}, {"streams", 3}, {"use", 3}, {"availability", 2}, {"chick", 2}, {"chicks", 2}, {"dietary", 2}, {"Eastern", 2}, {"effects", 2}, {"examine", 2}, {"expect", 2}, {"high", 2}, {"important", 2}, {"isotope", 2}, {"items", 2}, {"length", 2}, {"local", 2}, {"low", 2}, {"measured", 2}, {"primary", 2}, {"producers", 2}, {"provide", 2}, {"rates", 2}, {"resources", 2}, {"synthesized", 2}, {"tissues", 2}, {"used", 2}}|>, "1500998" -> <|"AwardTitle" -> "Deformation/rigidity theory in von Neumann algebras and ergodic theory", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[73357, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Von Neumann algebras were introduced in the 1930s and 1940s in part as a tool for developing a mathematical foundation for quantum physics. Von Neumann algebras have since become a field of independent interest with further applications to areas of mathematics such as ergodic theory, Voiculescu's free probability theory, Jones's theory of subfactors and planar algebras, knot theory, and many others. The development of von Neumann algebras has also historically been closely connected to the study of measurable dynamics, and these connections have recently begun to reemerge in the presence of a newly developed rigidity phenomenon. The investigation of this rigidity phenomenon has since led to new connections between von Neumann algebras and other areas of mathematics. Furthering the development of rigidity theory will in turn lead to new insights and connections among these various fields, and it will provide opportunities to exploit this phenomenon in other areas. \n\nThis project will investigate the newly emerging deformation/rigidity theory in von Neumann algebras, as well as continue to explore the deep connection between this theory and ergodic theory. Deformation/rigidity theory, initiated by Popa in the early 2000s, has been extremely successful over the last decade in answering a number of longstanding problems in von Neumann algebras and ergodic theory. The juxtaposition between deformability properties such as Haagerup's property, free products, or unbounded cocycles, with rigidity properties such as so-called property T or the spectral gap allows one to discover hidden structure in a von Neumann algebra where both types of phenomena occur. This has led to new insight in the structural properties of these von Neumann algebras, and in turn has found applications to other areas such as measured group theory, or the theory of invariants. Developing alongside deformation/rigidity theory is the corresponding techniques applied to ergodic theory of group actions. This has already led to a number of striking results, and yet here the surface has only been scratched. This project will also investigate more fully these interactions.", "AwardID" -> "1500998", "Institution" -> Entity["NSFInstitution", "VanderbiltUniversity"], "Investigators" -> {Entity["NSFInvestigator", "JessePeterson"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "9150", "Text" -> "EXP PROG TO STIM COMP RES"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1500998&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 14}, {"algebras", 8}, {"Neumann", 8}, {"rigidity", 7}, {"von", 6}, {"areas", 4}, {"ergodic", 4}, {"connections", 3}, {"led", 3}, {"new", 3}, {"phenomenon", 3}, {"properties", 3}, {"applications", 2}, {"deformation", 2}, {"development", 2}, {"free", 2}, {"group", 2}, {"investigate", 2}, {"mathematics", 2}, {"newly", 2}, {"number", 2}, {"project", 2}, {"property", 2}, {"turn", 2}, {"Von", 2}}|>, "1501000" -> <|"AwardTitle" -> "Hydrodynamics of Liquid Crystals and Extremum Problems for Eigenvalues", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2020, 5, 31}], "AwardAmount" -> Quantity[250000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This proposal is for a deep theoretical study on a class of complex fluids including both the liquid crystals which have been widely used in display devices and charged biological fluids which are extremely important in modern medicine and life sciences. Of particular interests are their intriguing and complex dynamical phenomena as well as formations of patterns and singularities. The modeling, analysis and simulations involved in understanding these complex fluids are theoretically very important and challenging. It needs new ideas and methods, and hence it would advance our knowledge which would be applicable to many other scientific problems as well.\n\nMore specifically, the proposal consists of two parts. The first part is to study partial differential equations that describe the hydrodynamics of liquid crystals and related complex fluid models. The main focus of this part of the research will be to study global existence of suitable weak solutions of liquid crystal flows in the Ericksen-Leslie theory; the global existence of solutions of Oldroyd B-model of incompressible visco-elastic fluids; the inviscid incompressible magneto-hydrodynamic system and, in general, coupled nonlinear dynamics of fluids with other geometric objects. The second part is to study a large class of extremum problems of elliptic eigenvalues. Such problems also arise in optimal designs, pattern formations and other applications in material sciences and condense matter physics. The partial differential equations (PDE) that the PI plans to study involve nonlinear couplings between equations that describe transport, phase-field, mapping or geometric object's evolutions and that of Navier Stokes equations. They may be of both parabolic and hyperbolic nature and possess singularities or multiple scales. The variational problems for eigenvalues and eigenfunctions that linked with underlying domains are classical and fundamental. These are fascinating and challenging problems that require new ideas and methods, which could lead to new directions of research or programs in the analysis of PDE and calculus of variations. The proposed research activity is an important and integral part of the PI's training program of under-graduate, graduate, and post-doctoral students.", "AwardID" -> "1501000", "Institution" -> Entity["NSFInstitution", "NewYorkUniversity"], "Investigators" -> {Entity["NSFInvestigator", "Fang-HuaLin"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501000&HistoricalAwards=false"], "KeywordTally" -> {{"fluids", 5}, {"problems", 5}, {"study", 5}, {"complex", 4}, {"equations", 4}, {"important", 3}, {"liquid", 3}, {"new", 3}, {"research", 3}, {"analysis", 2}, {"challenging", 2}, {"class", 2}, {"crystals", 2}, {"describe", 2}, {"differential", 2}, {"eigenvalues", 2}, {"existence", 2}, {"formations", 2}, {"geometric", 2}, {"global", 2}, {"ideas", 2}, {"incompressible", 2}, {"methods", 2}, {"nonlinear", 2}, {"partial", 2}, {"PDE", 2}, {"proposal", 2}, {"sciences", 2}, {"singularities", 2}, {"solutions", 2}}|>, "1501001" -> <|"AwardTitle" -> "Questions on Algebraic Operads and Related Structures", "AwardEffectiveDate" -> DateObject[{2015, 8, 1}], "AwardExpirationDate" -> DateObject[{2018, 7, 31}], "AwardAmount" -> Quantity[160001, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Andrew D. Pollington", "Abstract" -> "Operads and their generalizations are used to describe a large class of algebraic structures. They play an important role in the study of various geometric objects, in tackling foundational questions of quantum mechanics, and in addressing certain questions in number theory. This research project aims to resolve important open questions in this area. In addition to pursuing the research project, the investigator will advise graduate student research projects and expects to supervise undergraduate research projects as well. Jointly with coauthors, the investigator is writing a graduate level textbook on deformation quantization of symplectic manifolds. \n\nThe principal investigator is tackling the Deligne-Drinfeld conjecture on the Grothendieck-Teichmueller Lie algebra using the deformation complex of the operad governing Gerstenhaber algebras and Kontsevich's graph complex related to deformation quantization. The PI is working on a circle of problems related to the modular operad which is obtained by applying the Feynman transform to the operad governing commutative algebras. The PI also works on the problem of deformation quantization over a graded base and studies a higher categorical structure on homotopy algebras. The study of the Grothendieck-Teichmueller Lie algebra is motivated by its links to deformation quantization, the absolute Galois group of rational numbers and the theory of motives. Questions about the Feynman transform of the operad governing commutative algebras are motivated by the study of spaces of long knots.", "AwardID" -> "1501001", "Institution" -> Entity["NSFInstitution", "TempleUniversity"], "Investigators" -> {Entity["NSFInvestigator", "GoldenRichard"], Entity["NSFInvestigator", "VassilRoussev"], Entity["NSFInvestigator", "VasiliyDolgushev"], Entity["NSFInvestigator", "IrfanAhmed"]}, "ProgramElements" -> {{"Code" -> "1264", "Text" -> "ALGEBRA,NUMBER THEORY,AND COM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501001&HistoricalAwards=false"], "KeywordTally" -> {{"deformation", 5}, {"algebras", 4}, {"operad", 4}, {"quantization", 4}, {"research", 4}, {"governing", 3}, {"investigator", 3}, {"questions", 3}, {"study", 3}, {"algebra", 2}, {"commutative", 2}, {"complex", 2}, {"Feynman", 2}, {"graduate", 2}, {"Grothendieck-Teichmueller", 2}, {"important", 2}, {"Lie", 2}, {"motivated", 2}, {"PI", 2}, {"project", 2}, {"projects", 2}, {"related", 2}, {"tackling", 2}, {"theory", 2}, {"transform", 2}}|>, "1501004" -> <|"AwardTitle" -> "Nonlinear Elliptic Equations and Systems and Applications", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2020, 5, 31}], "AwardAmount" -> Quantity[259038, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Partial differential equations arise naturally in physics, engineering, geometry, and many other fields, and they form the basis for modeling many phenomena in the physical world. The proposed work concern nonlinear partial differential equations, which are especially important due to the nonlinear effects they are used to model. For instance, such equations turn up in the study of composite materials. This project will contribute to a basic understanding of fully nonlinear elliptic equations, thereby providing scientists and engineers with sharpened insight into various physical processes and ultimately enhancing the quality of, say, consumer products manufactured from composites. As part of the project, the principal investigator will train Ph.D. students, many of whom are expected to continue their careers as educators. They, in turn, will convey to even younger generations both their mathematical knowledge and the long-term value of mathematical research not only to science and engineering but also, in the end, to society.\n\n\nThe PI proposes to investigate the compactness of conformal metrics on a Riemannian manifold having constant sigma-k curvature for k larger than 1 and less than half of the dimension of the manifold. For k greater than or equal to half of the dimension of the manifold, or when the manifold is locally conformally flat, the compactness result has been proved. A success in establishing the compactness results would lead to new existence results on conformal metrics with constant sigma-k curvature. A related problem on compactness of solutions to the constant Q-curvature equations on Riemannian manifolds is also proposed. The PI has also proposed to study elliptic systems arising from composite material. The approach to the study of the compactness of solutions is to give a fine analysis of blow up solutions to the type of nonlinear elliptic equations on manifolds. Efforts will be made in advancing further and deeper understanding of solutions of conformally invariant equations.", "AwardID" -> "1501004", "Institution" -> Entity["NSFInstitution", "RutgersUniversityNewBrunswick"], "Investigators" -> {Entity["NSFInvestigator", "YanyanLi"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501004&HistoricalAwards=false"], "KeywordTally" -> {{"equations", 7}, {"compactness", 5}, {"manifold", 4}, {"nonlinear", 4}, {"solutions", 4}, {"constant", 3}, {"elliptic", 3}, {"proposed", 3}, {"study", 3}, {"composite", 2}, {"conformal", 2}, {"conformally", 2}, {"curvature", 2}, {"differential", 2}, {"dimension", 2}, {"engineering", 2}, {"half", 2}, {"k", 2}, {"manifolds", 2}, {"mathematical", 2}, {"metrics", 2}, {"physical", 2}, {"PI", 2}, {"project", 2}, {"results", 2}, {"Riemannian", 2}, {"sigma-k", 2}, {"turn", 2}, {"understanding", 2}}|>, "1501007" -> <|"AwardTitle" -> "Variational Problems and Dynamics", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[81038, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "The research is aimed at solving mathematical problems that are not only significant as mathematics, but that have been suggested by problems arising in physics and biology. The analysis of the equations governing physical and biological processes often requires a precise quantitative understanding of the relative sizes of various quantities involved in these processes, and this is provided by mathematical inequalities, often of a geometric nature. The quest for a better understanding of these processes is in part quest for new and more precise mathematical inequalities. One way of discovering and proving such mathematical inequalities, which is central to the project, is through the consideration of auxiliary dynamical processes that evolve the state of a system into a form that is amenable to analysis. This area of research has been fruitful not only in producing results that are of interest to a wider scientific community, but also in engaging the interest of Ph.D. students. The intellectual merit of the research is that it will produce not only significant new mathematics, but results that are relevant to physical and biological sciences as well. These applications in other fields guarantee a broad impact of the work, which is further enhanced by the involvement of students, contributing to training of the next generation of researchers. \n\nAmong the many nonlinear evolution equations that arise in the description of physical and biological systems are the Boltzmann equation and the Keller-Segel equations for chemotaxis. For both of these, an essential source of information on the behavior of solutions is a priori functional inequalities. For example, solutions of the Boltzmann equation tend towards equilibrium solutions, and the rate at which this happens is governed by an inequality relating relative entropy and the entropy production forced by the evolution. Such functional inequalities are established by completely solving a variational problem: finding the minimum value of some functional, determining the full set of minimizing functions, and finally, proving results that assert that if the value of a functional is close to the optimal value, then its argument must be close to an optimizer. Such complete solutions of variational problems are not only of interest for studying the evolution of physical systems, but also, variational problems can sometimes be best solved by studying an appropriate dynamics associated with them. This interplay between nonlinear dynamics and variational problems has been the source of much recent progress. This project focuses on variational problems and on nonlinear evolution equations, with emphasis on those problems in which the investigator expects a particularly fruitful interplay. A second focus is on operator and trace inequalities for quantum systems. Investigation of these is motivated by problems in quantum statistical mechanics and quantum information theory, and again there is close interplay between quantum dynamics and the inequalities to be investigated, except that here functions are replaced by operators and non-commutativity issues arise.", "AwardID" -> "1501007", "Institution" -> Entity["NSFInstitution", "RutgersUniversityNewBrunswick"], "Investigators" -> {Entity["NSFInvestigator", "EricCarlen"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501007&HistoricalAwards=false"], "KeywordTally" -> {{"problems", 8}, {"inequalities", 7}, {"variational", 5}, {"equations", 4}, {"evolution", 4}, {"functional", 4}, {"mathematical", 4}, {"physical", 4}, {"processes", 4}, {"quantum", 4}, {"solutions", 4}, {"biological", 3}, {"close", 3}, {"dynamics", 3}, {"interplay", 3}, {"nonlinear", 3}, {"research", 3}, {"results", 3}, {"systems", 3}, {"value", 3}, {"analysis", 2}, {"arise", 2}, {"Boltzmann", 2}, {"entropy", 2}, {"equation", 2}, {"fruitful", 2}, {"functions", 2}, {"information", 2}, {"mathematics", 2}, {"new", 2}, {"precise", 2}, {"project", 2}, {"proving", 2}, {"quest", 2}, {"relative", 2}, {"significant", 2}, {"solving", 2}, {"source", 2}, {"students", 2}, {"studying", 2}, {"understanding", 2}}|>, "1501012" -> <|"AwardTitle" -> "DISSERTATION RESEARCH: The effects of multi-species interactions on the community structure of parasites", "AwardEffectiveDate" -> DateObject[{2015, 6, 15}], "AwardExpirationDate" -> DateObject[{2017, 5, 31}], "AwardAmount" -> Quantity[16293, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "08010208", "ProgramOfficer" -> "George Malanson", "Abstract" -> "Research on infectious diseases typically focuses on single-parasite infections. However, most individuals are co-infected with multiple parasite species, and parasites interact with one another within hosts. These interactions may profoundly impact the outcome of parasite infections. For example, parasites that directly compete with one another for the same resource may inhibit each other's persistence. This project will examine the direct and indirect interactions of multiple intestinal parasites in school children in southern Vietnam. The prevalence of parasites will be quantified and interactions examined through immunological assays. This research will expand from the idea that hosts harbor only one infection at a time and will provide a better understanding of the patterns and processes shaping within-host parasite communities. Ultimately, by considering hosts infected with multiple parasite species, this research may reshape the design and implementation of global health interventions against intestinal parasites; in the short term it will aid in local public health efforts in Vietnam. The project will also advance the field of disease ecology by the study of population-level processes. It will support the training of a graduate student while increasing international colloboration.\n\nCompared to single-parasite infections, multi-species infection interactions can profoundly impact host fitness, parasite transmission, and disease dynamics in unexpected ways. This project will investigate the effects of parasitic helminth infections on subsequent colonization by diarrheal pathogens. The first step will determine the composition of parasite communities using PCR on stool samples. The second step will use sequence the 16S rRNA gene to generate data on the taxonomy of the gut microbiota, and blood and stool samples will be analyzed for immune markers. As helminth infections occur in over 2 billion people worldwide, understanding diarrheal diseases in the context of helminth co-infections may help explain the heterogeneity in parasite burden and disease severity found amongst individual hosts and shape patterns of disease dynamics at the population level. Knowledge about such within-host parasite interactions will also have important implications for studies in disease ecology and will be important for effective management of human and animal diseases in co-infected populations. This project will foster collaborations between U.S., U.K., and Vietnamese universities and will train students in parasitological, immunological, and ecological methods. The overall study findings will be published in both English and Vietnamese and will also be conveyed to the Vietnamese community and public health system through outreach programs.", "AwardID" -> "1501012", "Institution" -> Entity["NSFInstitution", "PrincetonUniversity"], "Investigators" -> {Entity["NSFInvestigator", "AndreaGraham"], Entity["NSFInvestigator", "JacquelineLeung"]}, "ProgramElements" -> {{"Code" -> "1182", "Text" -> "POP & COMMUNITY ECOL PROG"}}, "ProgramReferences" -> {{"Code" -> "9169", "Text" -> "BIODIVERSITY AND ECOSYSTEM DYNAMICS"}, {"Code" -> "9179", "Text" -> "GRADUATE INVOLVEMENT"}, {"Code" -> "EGCH", "Text" -> "ENVIRONMENT AND GLOBAL CHANGE"}, {"Code" -> "SMET", "Text" -> "SCIENCE, MATH, ENG & TECH EDUCATION"}}, "Directorate" -> "Direct For Biological Sciences", "Division" -> "Division Of Environmental Biology", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501012&HistoricalAwards=false"], "KeywordTally" -> {{"parasite", 8}, {"disease", 5}, {"infections", 5}, {"interactions", 5}, {"parasites", 5}, {"hosts", 4}, {"project", 4}, {"diseases", 3}, {"health", 3}, {"helminth", 3}, {"multiple", 3}, {"Vietnamese", 3}, {"co-infected", 2}, {"communities", 2}, {"diarrheal", 2}, {"dynamics", 2}, {"ecology", 2}, {"-host", 2}, {"immunological", 2}, {"impact", 2}, {"important", 2}, {"infection", 2}, {"intestinal", 2}, {"patterns", 2}, {"processes", 2}, {"profoundly", 2}, {"public", 2}, {"research", 2}, {"samples", 2}, {"single-parasite", 2}, {"species", 2}, {"step", 2}, {"stool", 2}, {"study", 2}, {"understanding", 2}, {"Vietnam", 2}}|>, "1501013" -> <|"AwardTitle" -> "Summer Symposium in Real Analysis 39", "AwardEffectiveDate" -> DateObject[{2015, 1, 1}], "AwardExpirationDate" -> DateObject[{2015, 12, 31}], "AwardAmount" -> Quantity[19390, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "This award provides funding to help defray the expenses of participants in the \"Summer Symposium in Real Analysis 39\" that will be held June 8-13, 2015, on the campus of St. Olaf College. This conference is the thirty-ninth in a series that has evolved into one of the major venues internationally for the presentation of research developments in real analysis and related areas. \n\nThe scientific program for the 2015 Symposium covers a broad array of topics, ranging from regularity issues for partial differential equations to Morse-Sard-type results, from questions in geometric measure theory to topics in combinatorial and set theoretic analysis. The featured speakers are Marianna Csornyei (University of Chicago), Alexander Olevskii (University of Tel Aviv), and Miklos Laczkovich (Eotovos Lorand University). The conference program provides ample opportunity for graduate students, postdocs, and other young scientists to present their work. Proceedings of the Symposium will be made available on-line.\n\nConference web site: http://www.stolaf.edu/analysis/", "AwardID" -> "1501013", "Institution" -> Entity["NSFInstitution", "SaintOlafCollege"], "Investigators" -> {Entity["NSFInvestigator", "MariannaCsornyei"], Entity["NSFInvestigator", "BruceHanson"], Entity["NSFInvestigator", "PaulHumke"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501013&HistoricalAwards=false"], "KeywordTally" -> {{"Symposium", 3}, {"University", 3}, {"2015", 2}, {"analysis", 2}, {"conference", 2}, {"program", 2}, {"provides", 2}, {"topics", 2}}|>, "1501019" -> <|"AwardTitle" -> "Weak Turbulence", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[100001, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Turbulence is the phenomenon by which a fluid flow, initially very smooth, can develop smaller and smaller eddies, structures at smaller and smaller scales, until it looks completely chaotic. Though anybody can observe this phenomenon, and though it is of paramount importance in physics, aerospace engineering, etc., it is very poorly understood at a conceptual level. Weak turbulence is a related phenomenon, which is also poorly understood, but which might be theoretically more approachable. Rather than fluid flows, it describes situations where waves interact. The aim of this proposal is to develop theoretical tools, and apply them to concrete physical examples, leading to a deeper understanding of weak turbulence.\n\nTo be more specific, the main object of focus will be the nonlinear Schroedinger equation set on a compact domain, which is one of the simplest and most used models to describe nonlinear wave, or dispersive phenomena. It is believed by physicists that the right regime to observe weak turbulence involves three limits: weakly nonlinear (small data), big box (large domain), random phases (decorrelation of the Fourier modes in a statistical sense). The aim of this project is to investigate how these three limiting procedures can be made rigorous. It involves spectral questions (understanding the eigenvalues and eigenmodes of the Laplacian on domains), nonlinear aspects (how these eigenmodes interact) and statistical questions (finding the right probabilistic description of the stationary state).", "AwardID" -> "1501019", "Institution" -> Entity["NSFInstitution", "NewYorkUniversity"], "Investigators" -> {Entity["NSFInvestigator", "PierreGermain"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501019&HistoricalAwards=false"], "KeywordTally" -> {{"nonlinear", 4}, {"smaller", 4}, {"phenomenon", 3}, {"aim", 2}, {"develop", 2}, {"domain", 2}, {"eigenmodes", 2}, {"fluid", 2}, {"interact", 2}, {"involves", 2}, {"observe", 2}, {"poorly", 2}, {"questions", 2}, {"right", 2}, {"statistical", 2}, {"turbulence", 2}, {"understanding", 2}, {"understood", 2}, {"weak", 2}}|>, "1501020" -> <|"AwardTitle" -> "UNC PDE Mini-Schools", "AwardEffectiveDate" -> DateObject[{2015, 2, 1}], "AwardExpirationDate" -> DateObject[{2017, 1, 31}], "AwardAmount" -> Quantity[49000, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "Abstract (Christianson, 1501020): \n\nThis award provides funding for a sequence of mini-schools during 2015-2017, to be held at the University of North Carolina. The three mini-schools in 2015 will be held held during March 4-6, 2015 (tentative), April 8-10, 2015 and summer of 2015 respectively.\n\nThrough the mini-schools, intimate interaction and collaboration will be established between members at all levels of the University of North Carolina Partial Differential Equations group with members at all levels of other elite research groups with allied interests. The tentative principal speakers for 2015 are: Gunther Uhlmann, Alexandru Ionescu, and Steve Zelditch. During each mini-school, the principal speaker will give a series of three or more lectures over the course of 2-3 days on an important topic in the fields of geometric analysis and partial differential equations. Funded participants will be chosen by the organizing committee in collaboration with the principal speaker. Several funded participants will give satellite talks complementing the principal speaker's lectures. More information will be provided at https://math.unc.edu/seminars-and-colloquia/seminar.", "AwardID" -> "1501020", "Institution" -> Entity["NSFInstitution", "UniversityOfNorthCarolinaAtChapelHill"], "Investigators" -> {Entity["NSFInvestigator", "JasonMetcalfe"], Entity["NSFInvestigator", "HansChristianson"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501020&HistoricalAwards=false"], "KeywordTally" -> {{"2015", 5}, {"principal", 4}, {"held", 3}, {"mini-schools", 3}, {"Carolina", 2}, {"collaboration", 2}, {"lectures", 2}, {"levels", 2}, {"members", 2}, {"North", 2}, {"participants", 2}, {"speaker", 2}, {"tentative", 2}, {"University", 2}}|>, "1501024" -> <|"AwardTitle" -> "Function theory in CR geometry and partial differential equations", "AwardEffectiveDate" -> DateObject[{2015, 9, 1}], "AwardExpirationDate" -> DateObject[{2018, 8, 31}], "AwardAmount" -> Quantity[118348, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Edward Taylor", "Abstract" -> "Function theory in complex analysis has important applications to other branches of mathematics including algebraic geometry, applied mathematics, as well as to other disciplines, such as physics and engineering. For instance, in problems arising from electric fields, various geometric conditions can always be expressed in terms of functions of complex variables. By employing appropriate conformal maps, many inconvenient geometric configurations can be transformed to rather easy formats and hence be completely solved. Some other types of real-world phenomena are modeled as solutions to certain partial differential equations. Methods developed in complex analysis, such as Fourier analysis, have played fundamental roles in solving those equations and giving interpretations for solutions. The current project will address related problems in holomorphic function theory. Progress of the project will help us understand more precisely properties of conformal maps in higher dimensions and explore new methods that can be applied into other fields. \n\nThe PI proposes to study a variety of problems in several complex variables and the corresponding partial differential equations, together with her collaborators. More specifically, the PI will investigate rigidity and classification problems of CR embeddings between some special types of CR manifolds, such as (generalized) Heisenberg hypersurfaces. Since transversality property of CR mappings is closely related to CR embeddability, she also plans to continue the work on CR transversality along the line of the conjecture of Baouendi-Huang for Levi non-degenerate hypersurfaces of higher codimension. On the aspect of partial differential equations, the PI will work on regularity of solutions to Cauchy-Riemann equations over pseudoconvex domains through the method of integral representation theory. The method will involve strong correlation between holomorphic function theory and the geometry of the domains. The PI is also interested in the regularity problem for solutions to some Beltrami equations, as well as solvability and regularity to some general types of nonlinear elliptic complex partial differential equations on Heisenberg hypersurfaces.", "AwardID" -> "1501024", "Institution" -> Entity["NSFInstitution", "PurdueUniversity"], "Investigators" -> {Entity["NSFInvestigator", "YuanZhang"]}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501024&HistoricalAwards=false"], "KeywordTally" -> {{"equations", 7}, {"complex", 5}, {"CR", 5}, {"differential", 4}, {"partial", 4}, {"PI", 4}, {"problems", 4}, {"solutions", 4}, {"theory", 4}, {"analysis", 3}, {"hypersurfaces", 3}, {"regularity", 3}, {"types", 3}, {"applied", 2}, {"conformal", 2}, {"domains", 2}, {"fields", 2}, {"function", 2}, {"geometric", 2}, {"geometry", 2}, {"Heisenberg", 2}, {"higher", 2}, {"holomorphic", 2}, {"maps", 2}, {"mathematics", 2}, {"method", 2}, {"project", 2}, {"related", 2}, {"transversality", 2}, {"variables", 2}, {"work", 2}}|>, "1501031" -> <|"AwardTitle" -> "Boundary Problems in the Boltzmann theory", "AwardEffectiveDate" -> DateObject[{2015, 6, 1}], "AwardExpirationDate" -> DateObject[{2018, 5, 31}], "AwardAmount" -> Quantity[118245, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The kinetic theory and its models such as the Boltzmann equation and Vlasov equations have played an important role in the understanding of problems in gas dynamics, plasma physics, and fluid equations. In many physical situations, the particles in various models interact with boundaries, and this interaction creates several interesting phenomena such as the formation of singularities. In general, boundary effects may not stay only near the boundary but also impact on the whole interior dynamics. Therefore the boundary effects are important and have rich application in many cases. However, boundary problems in kinetic models are mathematically challenging due to their singular nature. This project aims to develop new mathematical tools to handle these problems.\n\nThis research project studies several important boundary problems arising in kinetic models and fluid equations. The first topic regards optimal regularity of Boltzmann solutions in bounded domains with several physical boundary conditions for both dynamical and stationary problems. The second topic concerns the boundary-field interaction in kinetic models such as Vlasov-Poisson-Boltzmann systems. The third topic is to understand the relation between steady Boltzmann solutions and the incompressible Navier-Stokes-Fourier systems in the presence of a boundary when the mean free path is sufficiently small. The last topic concerns fluid-material interaction such as surfactant dynamics on viscous surface waves. Results of the project are expected to improve modeling capabilities for a wide range of problems of interest to other scientists and engineers.", "AwardID" -> "1501031", "Institution" -> Entity["NSFInstitution", "UniversityOfWisconsin-Madison"], "Investigators" -> {Entity["NSFInvestigator", "ChanwooKim"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501031&HistoricalAwards=false"], "KeywordTally" -> {{"boundary", 7}, {"models", 5}, {"problems", 5}, {"kinetic", 4}, {"topic", 4}, {"Boltzmann", 3}, {"dynamics", 3}, {"equations", 3}, {"important", 3}, {"interaction", 3}, {"project", 3}, {"concerns", 2}, {"effects", 2}, {"fluid", 2}, {"physical", 2}, {"solutions", 2}, {"systems", 2}}|>, "1501036" -> <|"AwardTitle" -> "Treeable Equivalence Relations and the Use of Probability Groups in Arithmetic Combinatorics", "AwardEffectiveDate" -> DateObject[{2015, 5, 15}], "AwardExpirationDate" -> DateObject[{2018, 4, 30}], "AwardAmount" -> Quantity[85520, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Tomek Bartoszynski", "Abstract" -> "This is a research project at the interface of the mathematical topics of set theory, combinatorics, and analysis. The research contains three projects involving two main areas of mathematics: descriptive set theory and ergodic Ramsey theory. The first two of the research projects lie in the theory of definable equivalence relations, which provides a general framework for understanding the nature of classification of mathematical objects up to some notion of equivalence; due to its broad scope, it has natural interactions with many areas of mathematics. These two projects are devoted to studying an important subclass of definable equivalence relations and whether slight extensions of the members of this subclass still belong to it. The third project features a new method for obtaining statements in arithmetic combinatorics similar in nature to a celebrated theorem of Szemeredi, which roughly states that any non-negligible subset of integers retains much of the additive structure of the entire set of integers.\n\nIn the theory of definable equivalence relations on Polish spaces, a central place is occupied by countable Borel equivalence relations, an important subclass of which is that of treeable equivalence relations. The first two projects investigate the question of closure of this subclass under finite index extensions in two different contexts: Borel and measure-theoretic. The former involves Borel combinatorics and possibly Borel games, whereas the latter is tightly connected with ergodic theory and the theory of cost of equivalence relations, and may require nontrivial machinery from geometric group theory. The third project lies in ergodic Ramsey theory and its goal is to obtain multiple recurrence results for amenable groups via a correspondence principle provided by nonstandard analysis. This is done by transferring recurrence statements from a given amenable group to a more convenient setting of probability groups by taking the ultrapower of the original group and equipping it with Loeb measure. The latter, being countably additive, presents the main advantage of the probability group over the original amenable group equipped with only a finitely additive density function, enabling integration over the group and the use of Fubini's theorem.", "AwardID" -> "1501036", "Institution" -> Entity["NSFInstitution", "UniversityOfIllinoisAtUrbana-Champaign"], "Investigators" -> {Entity["NSFInvestigator", "AnushTserunyan"]}, "ProgramElements" -> {{"Code" -> "1268", "Text" -> "FOUNDATIONS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501036&HistoricalAwards=false"], "KeywordTally" -> {{"theory", 9}, {"equivalence", 7}, {"group", 6}, {"relations", 6}, {"Borel", 4}, {"projects", 4}, {"subclass", 4}, {"additive", 3}, {"amenable", 3}, {"combinatorics", 3}, {"definable", 3}, {"ergodic", 3}, {"project", 3}, {"research", 3}, {"set", 3}, {"analysis", 2}, {"areas", 2}, {"extensions", 2}, {"groups", 2}, {"important", 2}, {"latter", 2}, {"main", 2}, {"mathematical", 2}, {"mathematics", 2}, {"nature", 2}, {"original", 2}, {"probability", 2}, {"Ramsey", 2}, {"recurrence", 2}, {"statements", 2}, {"theorem", 2}, {"third", 2}}|>, "1501039" -> <|"AwardTitle" -> "Graduate Student Topology and Geometry Conference", "AwardEffectiveDate" -> DateObject[{2015, 3, 1}], "AwardExpirationDate" -> DateObject[{2017, 2, 28}], "AwardAmount" -> Quantity[76952, "USDollars"], "AwardInstrument" -> "Standard Grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Christopher W. Stark", "Abstract" -> "The thirteenth annual Graduate Student Topology and Geometry Conference (GSTGC) is to be held March 29-March 30, 2015, at the University of Illinois Urbana-Champaign. This will be the largest GSTGC ever, with over 150 graduate students from across the country at various stages of their careers expected to attend. The schedule includes a broad range of talks: 24-32 graduate student 30 minute talks on expository and original research topics in geometry/topology; plenary speakers, Kathryn Hess (EPFL), Misha Kapovich (UC Davis), and Daniel Wise (McGill); and six invited young faculty speakers, Anna Marie Bohmann (Northwestern), Jeff Danciger (UT Austin), Jo Nelson (IAS), Vivek Schende (UC Berkeley), Hiro Lee Tanaka (Harvard) and Jing Tao (Oklahoma). This conference will include talks in many subfields of topology and geometry, including hyperbolic geometry, geometry of positive curvature, global analysis, 3-manifolds, homotopy theory, symplectic geometry, dynamics, knot theory, cobordism theory, category theory, Teichmuller theory, 4-manifolds, differential topology, geometric group theory, algebraic K-theory, and more.\n\nThis conference provides a venue for communication among young mathematicians from different geographic regions. Participants include graduate students at all stages of their careers. This is one of the few conferences in topology and geometry that is dedicated to graduate students. Student participants at this conference have the opportunity to learn about cutting edge research, to refine their communication and networking skills, and to establish collaborations with peers. Geometry and topology are fundamental mathematical fields with deep connections to many other areas of research, such as dynamical systems, physics, computer science, and mathematical biology. This conference serves to foster research and communication about research in these areas, and to enable and encourage graduate students in these fields.\n\nConference URL: http://www.math.illinois.edu/gstgc2015/", "AwardID" -> "1501039", "Institution" -> Entity["NSFInstitution", "UniversityOfIllinoisAtUrbana-Champaign"], "Investigators" -> {Entity["NSFInvestigator", "StevenBradlow"]}, "ProgramElements" -> {{"Code" -> "1267", "Text" -> "TOPOLOGY"}, {"Code" -> "1265", "Text" -> "GEOMETRIC ANALYSIS"}}, "ProgramReferences" -> {{"Code" -> "7556", "Text" -> "CONFERENCE AND WORKSHOPS"}}, "Directorate" -> "Direct For Mathematical & Physical Scien", "Division" -> "Division Of Mathematical Sciences", "GrantURL" -> Hyperlink["http://www.nsf.gov/awardsearch/showAward?AWD_ID=1501039&HistoricalAwards=false"], "KeywordTally" -> {{"geometry", 6}, {"theory", 6}, {"graduate", 5}, {"research", 5}, {"topology", 5}, {"conference", 4}, {"students", 4}, {"communication", 3}, {"talks", 3}, {"30", 2}, {"areas", 2}, {"careers", 2}, {"Geometry", 2}, {"GSTGC", 2}, {"include", 2}, {"mathematical", 2}, {"speakers", 2}, {"stages", 2}, {"Student", 2}, {"UC", 2}, {"young", 2}}|>, "1501041" -> <|"AwardTitle" -> "Research in Harmonic Analysis and Partial Differential Equations", "AwardEffectiveDate" -> DateObject[{2015, 5, 15}], "AwardExpirationDate" -> DateObject[{2018, 4, 30}], "AwardAmount" -> Quantity[246817, "USDollars"], "AwardInstrument" -> "Continuing grant", "OrganizationCode" -> "03040000", "ProgramOfficer" -> "Bruce P. Palka", "Abstract" -> "The principal investigator will undertake research in harmonic analysis and in the analysis of partial differential equations (PDE). Harmonic analysis has played major roles in the pure and applied sciences since Fourier's seminal work on the theory of heat diffusion, continuing on with Schrodinger's equation in quantum mechanics. It underlies a diverse array of tools widely used in science and engineering, and it offers the promise of further applications in the future. The proposed research deals with foundational issues that may help to underpin future applications. In PDE, the project will study the long-time dynamical properties of several fundamental equations describing diverse physical phenomenon. In particular, the nonlinear Schrodinger equation (NLS) models the transmission of data in fiber optic communication systems, and the Korteweg-de Vries equation (KdV) models surface water waves as well as ion-acoustic waves in a cold plasma. The so-called fractional NLS is used as a model describing charge transport in bio polymers like DNA. Proposed problems on near-linear behavior and smoothing are directly motivated by real world engineering problems in fiber optic communication systems, and the methods used are likely to be useful in a range of applications.\n\nIn harmonic analysis this project focuses on problems in Euclidean spaces centered around Lebesgue norm inequalities. One subject of on-going research is the Fourier restriction phenomenon and its applications to problems in PDE and geometric measure theory. In the PDE component of the project, the focus is on the dynamical properties of linear and nonlinear dispersive equations. Subjects of interest here are dispersive decay and smoothing estimates for Schrodinger and wave equations, and their applications to the stability problem for their nonlinear counterparts. Another topic is the regularity properties of the solutions of nonlinear dispersive PDE such as the KdV equation, the Zakharov system, and the fractional NLS. The principal investigator will continue to explore the smoothing effect of the dispersive linear group on bounded domains, and he will study applications to the regularity properties and long-time dynamics of the nonlinear solutions. Proposed applications are on the existence and regularity of global attractors, dispersive quantization/Talbot effect, bounds for higher order Sobolev norms, and controllability.", "AwardID" -> "1501041", "Institution" -> Entity["NSFInstitution", "UniversityOfIllinoisAtUrbana-Champaign"], "Investigators" -> {Entity["NSFInvestigator", "MehmetBurakErdogan"]}, "ProgramElements" -> {{"Code" -> "1281", "Text" -> "ANALYSIS PROGRAM"}}, "Directorate" -