This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences program (CFDA 47.049) supports $299,998 in fundamental and applied research on the use of probabilistic methods to study deterministic objects with sophisticated structure. The principal investigator plans to address several significant conjectures in areas like geometric and combinatorial group theory, differential geometry, and automorphic forms. The award will fund activities to train...
This National Science Foundation (NSF) Project Grant award, under the Mathematical and Physical Sciences (CFDA 47.049) program, will support research on stochastic methods and isoperimetric inequalities at Texas A&M University. The $238,406 award, active from July 2024 to June 2027, will develop techniques to bridge fundamental conjectures in Brunn-Minkowski theory and dual Brunn-Minkowski theory, with a focus on intersection bodies and higher-dimensional generalizations. The research aims...
This $204,372 federal Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports research on the potential theoretic aspects of complex geometry. The principal investigator will employ methods from potential theory, infinite-dimensional geometry, and geometric analysis to investigate a cluster of interconnected questions and conjectures in complex geometry. The project aims to advance scientific knowledge in this...
This $350,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research on stochastic algorithms and mathematical models for complex systems with random perturbations. The project, led by North Carolina State University, will develop new geometric frameworks and methodologies to effectively incorporate randomness into algorithms for solving various types of equilibrium problems, such as those arising in data...
The National Science Foundation (NSF) Division of Mathematical Sciences has awarded a $300,000 Project Grant to Cornell University to support research on stochastic models and their properties. The key objectives of this 3-year grant, which runs from July 15, 2023 to June 30, 2026, are to: Develop novel methodologies to characterize different types of orbits exhibited by Markov semigroups on Hilbert spaces, providing a comprehensive understanding of these structures. Utilize the classification...
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...
This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) grant award to Cornell University provides $118,236 in funding from July 1, 2024 to June 30, 2027. The project focuses on studying the fundamental properties and global behaviors of random processes that are defined by related geometric or algebraic structures, such as Riemannian manifolds and groups. This work aims to advance the understanding of randomness and its applications in areas like image...
This National Science Foundation (NSF) Division of Mathematical Sciences Project Grant award to Brown University, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $180,000 in funding from August 15, 2023 to July 31, 2026. The award supports fundamental research on random functions and stochastic processes on random graphs, including the analysis of roots of polynomials with random coefficients. The project also focuses on studying the...
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 for...
The National Science Foundation (NSF) awarded a $152,144 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Princeton University. The grant, titled "Structured Randomness: Random Matrices and Geometry," aims to develop general mathematical tools to explain the interplay between randomness and underlying structure in complex mathematical problems. The research will focus on two areas - random matrix theory and metric geometry - by leveraging...