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...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research to deepen the understanding of how geometric properties, especially curvature, influence solutions to geometric optimization problems. The $170,996 award to New York University, spanning June 2025 to May 2028, aims to advance the theory of isoperimetric problems and group structures in geometric analysis. Key focus areas include studying isoperimetric...
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 $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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program is supporting research by The Trustees of Columbia University in the City of New York to advance the theoretical understanding of partial differential equations, free boundary problems, and related mathematical concepts. The $273,927 award, with a performance period from July 1, 2024 to June 30, 2027, focuses on developing new methods and regularity theories for specific...
The National Science Foundation Division of Mathematical Sciences awarded Columbia University a $300,000 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research on entropy in optimal transport and finance from July 1, 2021 to June 30, 2024. The Mathematical and Physical Sciences program aims to promote progress in mathematics and the physical sciences to strengthen the nation's scientific enterprise. This award will...
The University of California, Santa Barbara will conduct research on eigenvalue comparison and integral curvature under a $234,436 project grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049). The three-year award beginning July 1, 2021 will support analysis of major problems in mathematics, such as classifying the curvature of manifolds. As part of its mission to strengthen the nation's scientific enterprise, the NSF Mathematical and...
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 $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...