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 Division of Mathematical Sciences awarded Princeton University a $101,060 Project Grant under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to support the research project "Geometric Analysis of Einstein Manifolds and Their Generalizations" from October 1, 2021 through May 31, 2022. Under this award, Princeton University researchers conducted mathematical and physical sciences research focused on geometric analysis of...
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,...
This $177,900 Project Grant, awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports research on discrete conformal geometry of polyhedral surfaces. The primary objective is to solve the discrete uniformization problem for all polyhedral surfaces without topological constraints. The research aims to integrate techniques from discrete and computational geometry, Riemann surface theory, convex geometry, and 3D hyperbolic...
This Project Grant award of $250,000 from the National Science Foundation's (CFDA 47.049 - Mathematical and Physical Sciences) supports research by the Pennsylvania State University (Penn State) to study various problems characterized by singularities and ill-posedness of partial differential equations modeling the behavior of incompressible fluids and elastic solids. The key focus areas of the research project are: (1) wall interactions in hydrodynamics models, (2) the combined effect of...
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 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...
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...
This $307,873 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will fund research into geometric, analytic, and algebraic aspects of real submanifolds in complex varieties and their symmetries from June 1, 2022 to May 31, 2025. The University of California, San Diego will study properties of various metrics and kernels related to Kähler-Einstein metrics on higher-dimensional spaces, with goals of characterizing domains and...
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...