The University of North Carolina at Chapel Hill received a $740,299 Project Grant award from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The funding will support research into complex Lagrangian geometry as a tool to study geometric questions and quantization arising at the intersection of geometry and topology. Specifically, the award will allow researchers to construct concrete models...
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 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research in differential equations and the geometry of manifolds. The award, totaling $223,343, will fund the principal investigator's work in three main areas: classification of gravitational instantons in 4 dimensions, understanding Gromov-Hausdorff limits of Einstein metrics in the collapsing case, and the study of higher-dimensional...
This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) Project Grant award of $169,408, starting on June 1, 2024 and ending on August 31, 2026, supports research at the University of North Carolina at Chapel Hill (UNC-CH) on nonlinear stochastic partial differential equations and their applications. The project aims to develop a mathematical understanding of these equations, which arise in complex dynamic phenomena like global economic shifts and turbulent...
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 $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research aimed at advancing the mathematical analysis of nonlinear partial differential equations. The research has three main focus areas: (1) studying fluid dynamics problems with free boundaries, such as water waves, tsunamis, and hurricanes; (2) investigating the dynamics of gases and plasmas under physical kinetic boundary conditions,...
This $115,718 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports advanced research into the algebraic and geometric properties of solutions to systems of polynomial equations. The primary goals of the project are to study the algebraic aspects of these solutions using non-archimedean geometry, investigate the complexity of curves within varieties of general type, and develop new non-archimedean...
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,...
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 National Science Foundation (NSF) Project Grant award provides $253,734 to The Johns Hopkins University to support research on the regularity of solutions to elliptic partial differential equations and generalized minimal submanifolds. The award focuses on two main mathematical objectives: studying unique continuation for solutions to elliptic PDEs and investigating the regularity theory for generalized minimal submanifolds. This research under the NSF's Mathematical and Physical Sciences...