This $141,540 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports research at the University of North Carolina at Chapel Hill (UNC-CH) to develop analytical and computational tools for data-driven applications. The project will focus on signal/image recovery from limited data, exploring how to build effective mathematical models and design efficient algorithms to extract insights. Additionally, the project will integrate...
The University of North Carolina at Chapel Hill received a $740,299 Project Grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The funding will support research into complex Lagrangian geometry as a tool to study geometric questions and quantization arising at the intersection of geometry and topology. Specifically, the award will allow researchers to construct concrete models...
The National Science Foundation (NSF) awarded a $112,949 Project Grant to The Trustees of the Stevens Institute of Technology to conduct research under the Mathematical and Physical Sciences (CFDA 47.049) program. The project, titled "Uniformization of Surfaces and Mapping Problems in Metric Spaces", aims to develop new mathematical approaches for understanding the geometry of non-smooth spaces, building on the classical Uniformization Theorem. The research will investigate methods...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $400,000 Project Grant to Duke University on August 1, 2023 under the Mathematical and Physical Sciences program (CFDA 47.049) to support innovative numerical methods for solving high-dimensional partial differential equations (PDEs). The key objectives of the 3-year project are to: (1) design and analyze neural-network parametrization for high-dimensional functions with symmetry constraints, and (2) develop and...
The National Science Foundation (NSF) awarded a $343,850 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Cincinnati. This 3-year grant, effective September 1, 2024, will fund research to develop new mathematical tools for analyzing the large-scale geometric behavior of non-smooth metric measure spaces, which have diverse applications across fields like fluid mechanics, neurophysiology, and fractal geometry. The project aims to enhance the...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill (UNC) a $185,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports a three-year research project to develop Hodge theoretic techniques for studying Knizhnik-Zamolodchikov differential equations, which link representation theory, algebraic geometry, and mathematical physics. Key research activities include developing...
This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) Project Grant award of $169,408, starting on June 1, 2024 and ending on August 31, 2026, supports research at the University of North Carolina at Chapel Hill (UNC-CH) on nonlinear stochastic partial differential equations and their applications. The project aims to develop a mathematical understanding of these equations, which arise in complex dynamic phenomena like global economic shifts and turbulent...
This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program provides $234,951 to the University of North Carolina at Chapel Hill to conduct research on fully nonlinear equations and minimal submanifolds in Lagrangian geometry. The project, which runs from August 2024 to July 2027, will generate research opportunities for graduate students and support the mentoring of graduate students and postdocs through interactive research...
This $300,000 Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) supports research to develop new mathematical techniques for optimization problems, particularly those arising in contemporary data science applications. The key products and services to be delivered include:
Extending classical mathematical methods like Lojasiewicz rescaling to design and analyze optimization algorithms in...
This $185,987 National Science Foundation Division of Mathematical Sciences Project Grant supports continued collaborative research in enumerative algebraic geometry at the University of North Carolina at Chapel Hill from August 1, 2022 through July 31, 2025.
Specifically, the investigators and their graduate students will further their work resolving outstanding questions in enumerative algebraic geometry through techniques including intersection theory, equivariant localization, symmetric...