The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $222,327 Project Grant to The Trustees of Princeton University, Office of Research and Project Administration to conduct research on the metric geometry and analysis of Einstein manifolds over a 3-year period from August 1, 2023 to July 31, 2026. The research project will focus on investigating the degenerations and quantitative behaviors of Einstein manifolds, building on prior work by the principal investigator...
The National Science Foundation awarded Princeton University a $152,347 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports collaborative research on algebraic geometry and singularities in positive and mixed characteristic from May 2021 to May 2023. As part of its mission to strengthen the nation's scientific enterprise and increase knowledge in the mathematical and physical sciences, the NSF program aims to promote progress in these fields...
The National Science Foundation Division of Mathematical Sciences awarded The Trustees of Princeton University $133,960 under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) for the project "K-STABILITY AND HIGHER DIMENSIONAL GEOMETRY" from June 1, 2021 to May 31, 2022. The award aimed to advance understanding of major problems in mathematics through research on K-stability and higher dimensional geometry to be conducted at Princeton University in...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $440,500 Project Grant to Stanford University to conduct research on various aspects of the Einstein equations, which govern the dynamics of spacetime geometry in general relativity. The research aims to study the solution regimes where gravity is very strong, including the presence of spacetime singularities and the interaction between matter fields and gravity. Specific research questions include the nature of...
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) awarded a $250,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to The Trustees of Princeton University Office of Research and Project Administration Division, doing business as Princeton University. This grant, awarded on June 1, 2024, will fund research centered on algebraic geometry and singularities in arithmetic settings, with the goal of developing new techniques to describe higher differential forms in positive...
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 $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 Project Grant award from the National Science Foundation's (CFDA 47.049) Mathematical and Physical Sciences program provides $150,000 to The Pennsylvania State University (Penn State) to conduct research on conformal invariants, Einstein manifolds, and their minimal submanifolds. The research project, which runs from July 2025 to June 2028, aims to use methods from conformal geometry to construct and classify geometric invariants that can control the behaviors of Einstein manifolds and...
The Trustees of Princeton University were awarded a $364,540 Project Grant from the National Science Foundation Division of Mathematical Sciences on August 1, 2021 to complete the project by July 31, 2024. The grant supports the project "UNUSUAL CONCENTRATION PHENOMENA IN PROBABILITY, ANALYSIS, AND GEOMETRY" under the Mathematical and Physical Sciences program (CFDA 47.049). This program aims to promote progress in the mathematical and physical sciences to strengthen the nation's...