This three-year, $239,774 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research at Stony Brook University on the uniformization and rigidity of fractal metric spaces and the complex plane. Specifically, the principal investigator will develop new techniques to better understand fractal objects with non-smooth, wrinkled or self-similar patterns applying in nature and data storage applications. This includes...
This three-year project grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $349,952, will support research into the curvature of four-dimensional manifolds at Stony Brook University from September 2022 through August 2025. Specifically, the principal investigator will investigate generalizations of Einstein's field equations of general relativity in the Riemannian setting without distinguishing between space and time. The research aims to...
This $350,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research to understand the structure and properties of large, complex collections of objects through geometric embedding and distortion analysis. The project will investigate fundamental questions about the growth rate of distortion required to represent objects in simpler geometric spaces, with applications in areas like algorithm design, social...
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...
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 Research Foundation For The State University of New York (RF SUNY), doing business as Stony Brook University, received a $417,872 National Science Foundation Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to support research in quasiconformal analysis, optimal triangulations, and fractal geometry from September 1, 2023 through August 31, 2026. Through this award, RF SUNY will develop algorithms to compute optimal angle bounds and practical triangulations 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 $292,481 federal Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences supports research into local-to-global principles in geometry. The principal investigator plans to apply methods from discrete mathematics, homotopy theory, and other fields to analyze the impact of positive curvature and symmetry on the global shape of high-dimensional geometric objects called manifolds. The research goals involve understanding the interaction between local...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $372,697 Project Grant to The Research Foundation for the State University of New York (RF SUNY), doing business as Stony Brook University, for the period of July 1, 2023 to June 30, 2026. The grant will fund research related to the topology and links of singularities, with applications in areas such as algebraic geometry, combinatorics, and the construction of exotic smooth 4-manifolds and knotted surfaces. The...
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,...