This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $296,600.00 to the University of Wisconsin-Madison to further the theoretical understanding of complex analysis of several variables. The key focus areas include studying the Gromov hyperbolicity of the Kobayashi metric, regularity properties of biholomorphic mappings, quantitative versions of the Hartogs' extension theorem and analytic continuation, and...
This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $165,000 to Syracuse University to conduct research on homological approaches to differential forms, differential operators, and transfer of algebra structures. The award will support the principal investigator's research on measures of singularity in algebraic geometry, focusing on differential forms, differential operators, cotangent complexes, and DG-algebra and...
This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $153,450 to Syracuse University to conduct research on singularities in commutative algebra and algebraic geometry. The research project, titled "Homotopical Methods and Cohomological Supports in Local Algebra," aims to leverage tools from homological algebra to gain deeper insights into the structural properties of commutative rings and study singularities in local...
Syracuse University was awarded a $123,073 Project Grant from the National Science Foundation (NSF) Division of Mathematical Sciences. The award is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049) and will fund research titled "CONVEX BODY SHAPE RECOVERY VIA GEOMETRIC MEASURES AND INEQUALITIES" from July 1, 2021 through May 31, 2023. Under this award, Syracuse University researchers will develop new techniques using geometric measures and inequalities 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 $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 federal Project Grant award, with an obligated amount of $285,100.00, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports fundamental and applied research by the principal investigator at the University of California, San Diego (UCSD) focused on invariant analysis in several complex variables, CR geometry, and complex geometry. Key research areas include investigating the Bergman metric,...
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 $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 from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) provides $223,640 to Syracuse University from July 1, 2025 to June 30, 2028 to develop new mathematical tools and refine existing methods to address longstanding challenges in the field of elastic deformations. The research aims to analyze the mathematical foundations of elastic deformations through the framework of Sobolev homeomorphisms, which serve as natural models for nonlinear...