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 $100,972 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports fundamental research on nonlinear partial differential equations and their applications in fields such as crystal growth, combustion, and game theory. The primary investigator (PI) will study the regularity, large-time behavior, and qualitative properties of solutions to these equations, which have connections to areas like the calculus of...
This $147,128 Project Grant awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences supports research focused on two key areas: tomographic problems and isoperimetric problems in convex geometry. The project, titled "Harmonic Analysis and Affine Isoperimetric Inequalities in Convex Geometry," seeks to address these mathematical problems using techniques from Fourier transform, Radon transform, and other fields. The award will fund research to develop new...
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 $299,999 Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), will support fundamental research on the rigidity and bounded cohomology of groups acting on nonpositively curved spaces. The principal investigator (PI) will focus on understanding the dynamical, topological, and geometric properties of infinite transformation groups that act in a distance-preserving manner on spaces like Euclidean and hyperbolic...
This $194,972 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program supports research at Emory University focused on addressing open problems in discrete geometry. The central aims are to study the covering and intersection properties of convex geometric objects and explore connections between discrete geometry and other mathematical fields. Key planned activities include mentoring undergraduate students, developing new mathematical...
This $280,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research in birational geometry at New York University from April 2022 through March 2025. Specifically, the principal investigator will use methods from Galois cohomology of function fields, properties of algebraic cycles over non-algebraically closed fields, K-theory, and degeneration techniques to advance understanding of rationality and stable...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on the isoperimetric problem in geometric analysis. The $170,996 award to New York University (NYU) aims to deepen the understanding of how geometric properties, especially curvature, influence solutions to geometric optimization problems. The project uses tools from geometric measure theory to study the isoperimetric structure of spaces...
This $473,736 National Science Foundation project grant under the Mathematical and Physical Sciences program (CFDA 47.049) will fund research into the role of symmetry and convexity in isoperimetric-type geometric questions in high dimensions, with potential applications in learning theory and other fields. Principal investigator at Georgia Tech Research Corporation will supervise postdocs, students, and organize seminars to investigate asymptotic geometry questions like the behavior of large...
This $142,565 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research on the study of manifolds, or geometric objects, with positive or non-negative curvature. The principal investigator (PI) at James Madison University aims to construct new examples of such manifolds and develop new methods for proving rigidity theorems about their properties. The project also includes broader impact activities like outreach,...