The University of California, Riverside (UC Riverside) received a $233,452 Project Grant award from the National Science Foundation (NSF) Directorate for Mathematical and Physical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049) to study the behavior of geometric and linear data associated with the solution sets of polynomials. The award will support research on the algebraic geometry and topological properties of moduli spaces of varieties and pairs, with a focus on...
The Regents of the University of California at Riverside received a $147,494 Project Grant award from the National Science Foundation Division of Mathematical Sciences on July 1, 2021 to complete work by June 30, 2024. The award supports the "HIGGS BUNDLES, SURFACE GROUPS, AND CONFORMAL LIMITS" project under the Mathematical and Physical Sciences program (CFDA 47.049). Through this funding, the University of California at Riverside will promote progress in the mathematical and physical...
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,...
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 $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research to develop new tools for studying the geometry and dynamics of physical systems. Key research focus areas include: Investigating the existence and properties of periodic orbits in four-dimensional phase spaces with three-dimensional energy levels Studying the geometry of phase spaces to determine when dynamical systems are equivalent...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports a research and training program at the University of California, Irvine (UC Irvine). The $998,809 award will fund a series of improvements and new additions to UC Irvine's undergraduate, graduate, and postdoctoral training programs in geometry and topology, which have applications in mathematical physics, data science, and video game design. The projects aim to...
This $115,718 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports advanced research into the algebraic and geometric properties of solutions to systems of polynomial equations. The primary goals of the project are to study the algebraic aspects of these solutions using non-archimedean geometry, investigate the complexity of curves within varieties of general type, and develop new non-archimedean...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $141,490 Project Grant to the University of California, Santa Cruz (UCSC) under the Mathematical and Physical Sciences program (CFDA 47.049). The project seeks to study the geometry and topology of spaces with Ricci curvature bounded below, including both smooth manifolds and singular spaces. Key focus areas include investigating the fundamental groups of complete and non-compact manifolds with non-negative Ricci...
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...