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...
This Project Grant award, valued at $220,000.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research by Brown University to study variational methods in singular geometry, with applications to phenomena like classical mechanics, geodesics, and harmonic maps. The project aims to develop new analytical techniques to investigate the properties of solutions to non-linear elliptic PDEs, and...
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...
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 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 $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 three-year National Science Foundation Project Grant of $197,999 supports research and education activities at Worcester Polytechnic Institute under the Mathematical and Physical Sciences program (CFDA 47.049). The award will fund the development of novel mathematical methods to analyze partial differential equations describing singularities in continuum mechanics and materials science systems. The principal investigator will extend differential inclusion theory on rigidity and flexibility,...
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 Project Grant award for $330,586, provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA No. 47.049), supports research on the geometric and metric properties of two-dimensional surfaces. The principal investigator (PI) at Cornell University will investigate the classification of surfaces under singular flat and hyperbolic metrics, as well as the associated moduli spaces and related mathematical...