This federal Project Grant award in the amount of $177,469.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Grant Program (CFDA #47.049). The award will support research into the geometry of moduli spaces from low-dimensional topology and applications, with a focus on three main directions: studying higher algebraic structures in instanton Floer homology, analyzing the properties of generalized Seiberg-Witten equations, and exploring the...
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 federal Project Grant award for $300,000.00, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program, supports research to significantly expand the investigator's work on applications of model theory to the study of geometric structures. The key objectives are to: 1) tackle major transcendence problems such as the Ax-Lindemann-Weierstrass and Ax-Schanuel conjectures for uniformizing functions of geometric structures in higher...
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 $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 $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 $195,929 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research to investigate canonical metrics and stability in complex geometry. The principal investigator at Rutgers, The State University aims to bridge connections between differential geometry and algebraic geometry in the study of projective manifolds and scalar curvature. Key research activities include exploring the Yau-Tian-Donaldson...
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 $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) awarded a $339,999 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to New York University (NYU) for research on geometric analysis and complex geometry. The award supports the principal investigator's work on studying geometric structures of complex manifolds, including Calabi-Yau manifolds, and investigating the nature of singularities that arise in Ricci flow - a geometric evolution equation. The research aims to enhance...