This $293,784 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental and applied research on fluctuating systems, random environments, and stochastic algorithms. The research aims to improve understanding and exploitation of randomness across diverse settings, including materials science, fluid dynamics, and machine learning. Key areas of focus include stochastic homogenization, stochastic partial...
This $300,000 Project Grant was awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program. The grant supports a research project at Brown University titled "Stochastic Nash Evolution," which aims to develop a new framework for the Nash embedding theorems to align the foundations of mathematics with cutting-edge scientific applications, especially in artificial intelligence. The project involves rigorous analysis of Riemannian...
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...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $200,000 to conduct fundamental research on mathematical models that describe complex interactions, growth, and motion in irregular environments with stochastic unpredictability. The goal is to discover general mathematical laws that govern such systems, which have implications for a wide range of real-world phenomena including traffic, communication networks,...
Brown University received a three-year $365,000 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will fund research into rare events and fluctuations in high-dimensional stochastic systems. Brown University researchers will study three classes of stochastic systems: large collections of interacting diffusions; high-dimensional measures such as random matrix ensembles;...
This Project Grant award, valued at $220,000.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research by Brown University to study variational methods in singular geometry, with applications to phenomena like classical mechanics, geodesics, and harmonic maps. The project aims to develop new analytical techniques to investigate the properties of solutions to non-linear elliptic PDEs, and...
This National Science Foundation Project Grant of $229,021 awarded on August 1, 2022 will support research at the University of Texas at Austin to develop mathematical frameworks in optimal transport applications to probability, machine learning, and kinetic theory through July 31, 2025. Under the Mathematical and Physical Sciences program (CFDA 47.049), the investigator will advance understanding of stochastic modeling, artificial intelligence algorithms, and kinetic theory by exploiting...
This $225,000 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research to advance the understanding of generative machine learning models and optimal transport algorithms. The principal investigator at Yale University will study the statistical and computational guarantees of rectified flow and diffusion models, explore connections between these models, and develop novel and improved algorithms to enhance the...
This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $193,202 to Columbia University from August 15, 2022 through July 31, 2025. The funding will support research investigating long-time behavior and large population limits of stochastic processes with random times. Specifically, the university will develop mathematical and computational tools to analyze complex interacting systems, with a focus on stochastic models involving...
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...