This Project Grant award from the National Science Foundation (NSF) under the Social, Behavioral, and Economic Sciences (CFDA 47.075) program provides $444,729 to the University of California Irvine (UC Irvine) to support research on the role of symmetry in physics. The project seeks to develop a systematic approach to understanding how symmetry principles guide the fundamental laws and equations of physics, and explore applications of this account to issues in areas like general relativity...
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 $271,119 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on complex Lagrangians, integrable systems, and quantization in relation to mirror symmetry. The University of California, Davis will lead a research group investigating mirror symmetry as it relates to symplectic geometry and complex algebraic geometry. The group will establish complex Lagrangian geometry as a tool to study geometric...
This $380,000 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research at the University of Illinois on mirror symmetry. The three-year award will fund a collaborative research group investigating mirror symmetry as it relates to symplectic geometry, complex algebraic geometry, and quantization. The group brings expertise from different mathematics areas and will use various techniques to construct concrete models...
This $300,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports quantitative research in symplectic geometry and its applications. The principal investigator (PI) at the University of Southern California (USC) will develop new tools and paradigms to study the quantitative aspects of symplectic geometry, including exploring links between symplectic geometry, algebraic curves, and cluster algebras. The project will...
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...
The National Science Foundation awarded Indiana University a $142,059 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research investigating ways to characterize, describe, and study spaces with many symmetries in various dynamical, geometric, and topological settings. The grant will support research exploiting connections between a wide range of mathematical areas to further understand fundamental structures related to lattices in Lie groups. Key...
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 $200,000 National Science Foundation Division of Mathematical Sciences Project Grant will support research and training in noncommutative algebra and geometry at the University of California Irvine from July 1, 2022 to June 30, 2025. The award will advance fundamental understanding of noncommutative algebraic structures that arise in geometry and physics. Researchers will develop new techniques to deduce good algebraic properties for geometrically constructed noncommutative algebras and...
This $330,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research into quantum groups, W-algebras, and Brauer-Kauffmann categories, with a focus on understanding the underlying mathematical symmetries that govern natural phenomena. The principal investigator will develop emerging theories and applications of I-quantum groups, including exploring braid group actions, Drinfeld presentations, and...