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...
This $210,000 Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports research on nonlinear partial differential equations, geometry, and convex analysis. The research aims to develop new analytical techniques with applications in geometry, physics, and algebraic geometry. Key focus areas include studying special Lagrangian submanifolds, Kähler-Einstein metrics, and Monge-Ampère type equations. The...
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 $246,525 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support fundamental research at the University of California, Irvine (UC Irvine) in the areas of spectral theory, several complex variables, and the geometry of Laplacian eigenfunctions. The key research objectives include investigations into the inverse spectral problem, the structure of Laplacian eigenfunctions, and the asymptotic behavior of Bergman...
This $120,000 Project Grant award, provided by the National Science Foundation (NSF) under the CFDA program 47.049 Mathematical and Physical Sciences, supports fundamental research on gravitational astrophysics and computational methods to advance scientific understanding of neutron stars, black holes, gravitational waves, and the large-scale structure of the universe. The award will fund a series of research projects at the University of California, San Diego (UCSD) focused on developing new...
The National Science Foundation (NSF) awarded a $369,218 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of California, San Diego (UCSD) to develop analytical methods for approximating the state of certain dynamical systems. The project aims to advance the understanding of quantitative aspects of the analysis of dynamical systems, with a focus on rigidity phenomena in the dynamics of group actions on structured spaces. Key research areas include...
This $270,000 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research in geometric representation theory and symplectic geometry at the University of California, Berkeley. The research aims to develop new tools and solve open problems in these mathematical fields, which draw inspiration from theoretical physics. Key research themes include investigating the cocenter of the affine Hecke category,...
The University of California, San Diego was awarded a $218,577 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research in the field of combinatorial representation theory from July 2023 through June 2026. Specifically, the principal investigator and collaborators will study objects that remain invariant under certain linear symmetries, seeking to extend...
This $300,000 National Science Foundation award under the Mathematical and Physical Sciences program (CFDA 47.049) supports research and education activities in the area of automorphic forms and exceptional algebraic structures at the University of California, San Diego from July 1, 2022 to June 30, 2027. The principal investigator will conduct three related research projects investigating half-integral weight modular forms on exceptional groups, modular forms on the exceptional group G2 with...
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, Bergman kernel, and the Cheng-Yau solution to the complex Monge-Ampère equation, as well as studying the Kohn Laplacian and the obstruction function on compact CR manifolds. The research aims to elucidate the connections between boundary geometry and analysis in complex spaces, with potential applications in mathematical and theoretical physics, systems engineering, and control theory. The award will also provide research opportunities for graduate students and postdoctoral fellows at UCSD. The project period runs from July 1, 2025 to June 30, 2028.