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 Project Grant from the National Science Foundation Division of Mathematical Sciences provides $278,485 to support research on rectifiability and fine geometry of sets, Radon measures, harmonic functions, and temperatures through July 2025. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), this award will advance four interconnected lines of inquiry. Researchers at the University of Connecticut will develop novel quantitative methods to study the geometry of...
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) 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 $285,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Utah to conduct research on hyperbolic geometry in two- and three-dimensional spaces. The project, running from August 1, 2024 to July 31, 2027, will focus on studying the geometry of hyperbolic 3-manifolds, including investigating the renormalized volume of such manifolds and the connection to the Weil-Petersson gradient flow. The...
This $237,552 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at Rutgers, The State University focused on advancing geometric analysis and partial differential equations in complex geometry. The key products and services to be delivered under this 3-year award include developing new conceptual frameworks and technical tools to provide insights into the geometric and analytic structures of the...
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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research to deepen the understanding of how geometric properties, especially curvature, influence solutions to geometric optimization problems. The $170,996 award to New York University, spanning June 2025 to May 2028, aims to advance the theory of isoperimetric problems and group structures in geometric analysis. Key focus areas include studying isoperimetric...
This Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), aims to advance the field of geometric and topological data analysis. The $270,000 award, with a performance period from July 15, 2025 to June 30, 2028, will fund research to tighten the connections between geometric/topological data analysis and statistics/machine learning. Key focus areas include developing large sample distribution theory for the Euler...
This $260,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on geometric limits in low dimensional geometry and topology at Boston College. The key objectives of the project are to analyze the global topology of the "space of all hyperbolic manifolds" and study the relationship between the "rank" of closed hyperbolic 3-manifolds and their geometry. In addition to the research...