This $369,910 National Science Foundation project grant supports research into the geometry of sets and measures in Euclidean and non-Euclidean spaces at Stony Brook University from June 1, 2022 to May 31, 2025. The awardee will investigate mathematical analogs to organizing and visualizing large data sets, transferring analysis tools from low-dimensional to higher-dimensional settings. Specific activities include exploring quantitative uniform rectifiability theory in novel metric spaces,...
This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences (CFDA 47.049) Federal Grant Program supports research at the interface of Fourier analysis and geometric measure theory. The $163,054 award to New York University, with a project period from April 2024 to August 2028, will explore connections between these two mathematical fields and their potential applications to other disciplines like dynamics and number theory. Key research components...
This three-year $215,251 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at the University of Tennessee to develop techniques in the field of analysis on metric spaces and geometric measure theory. The goals of the research are to relate integral bounds for discrete forms of curvature on non-smooth manifolds with locally Euclidean bi-Lipschitz parameterizations in dimensions greater than or equal to three,...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $350,358 to the University of Connecticut (UConn) to investigate geometric boundary value problems in general relativity. The research aims to advance understanding of the universe's structure by revealing connections between geometric PDEs and properties of the Laplace equation. Specifically, the project will address long-standing conjectures related to...
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...
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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research to develop new mathematical tools and understanding of the long-term dynamics and rigidity of certain infinite-volume mathematical systems. The $300,000 award to Yale University, to be completed by June 30, 2028, focuses on advancing the frontier of pure mathematics, with the goal of enabling applications in areas like data encryption, navigation, and...
This $239,068 Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program, supports research on geometric harmonic analysis and advances in Radon-like transforms at the University of Pennsylvania. The funded work focuses on developing new mathematical techniques and theoretical understanding related to Radon-like geometric averages and their applications in areas such as CT, SPECT, NMR imaging, radar, and sonar. Key goals...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $400,000 Project Grant to New York University (NYU) for the period of August 1, 2023 to July 31, 2026. The grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), focuses on two key areas: Studying geometric evolution equations, specifically mean curvature flow and Ricci flow, with a focus on different aspects of regularity. This research aims to address longstanding open problems at the...
This five-year $142,710 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will support research at Rutgers, The State University developing new tools in harmonic analysis, ergodic theory, and convex geometry. The Principal Investigator will investigate questions in ergodic theory related to the Furstenberg-Bergelson-Leibman conjecture for dynamical systems with nilpotent group structure. In harmonic analysis, the research will examine...