Project Grant 2303624
- The National Science Foundation (NSF) awarded a $254,266 Mathematical and Physical Sciences (CFDA 47.049) Project Grant to The Trustees of Columbia University in the City of New York to conduct research focused on "Scalar Curvature, Optimal Transport, and Geometric Inequalities." The project aims to advance understanding of the interplay between curvature and large-scale properties of manifolds, leveraging techniques from differential geometry and partial differential equations. Key...
- 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 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...
- 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...
- 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...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $141,490 Project Grant to the University of California, Santa Cruz (UCSC) under the Mathematical and Physical Sciences program (CFDA 47.049). The project seeks to study the geometry and topology of spaces with Ricci curvature bounded below, including both smooth manifolds and singular spaces. Key focus areas include investigating the fundamental groups of complete and non-compact manifolds with non-negative Ricci...
- 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...
- 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 $152,862 Project Grant under its Mathematical and Physical Sciences program (CFDA 47.049) to Rutgers, The State University of New Jersey - Newark Division. The grant will fund research focused on addressing open problems in geometric analysis and exploring their applications in fields such as geometry, topology, and mathematical physics. Key objectives include developing novel approaches in the regularity theory for linear and fully nonlinear...
- The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $399,998 Project Grant to the Massachusetts Institute of Technology (MIT) under the Mathematical and Physical Sciences program (CFDA 47.049) to fund research on singularities and rigidity in geometric evolution equations. The research focuses on geometric flows, which model the evolution of geometric objects like functions, surfaces, or Riemannian metrics over time using nonlinear generalizations of the classical...
This $380,500 project grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences supports research at New York University (NYU) on scalar curvature and geometric variational problems. The project aims to advance the understanding of scalar curvature, which describes the local bending of space, and its effects on the global properties of manifolds. Key focus areas include the obstruction problem for manifolds with positive scalar curvature, geometric comparison theorems using Riemannian polyhedra, the stable Bernstein problem for minimal surfaces, and the moduli space of positive scalar curvature metrics on 3-manifolds. This research has potential applications in general relativity and topology. The award duration is from August 1, 2023 to July 31, 2026.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $380.5k | 7/24/23 |