Project Grant H982300610080

This three-year project grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $303,805 to Texas A&M University to apply methods from combinatorial algebraic geometry to problems in spectral theory from mathematical physics. Specifically, the principal investigator (PI) will use algebraic geometry to study the spectrum of discrete periodic operators, an area with many open questions. The PI will also work to classify Galois groups...

This five-year, $350,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program will support research into the classification of locally homogeneous geometric structures on manifolds at the University of Maryland, College Park. The award reflects NSF's mission to promote progress in the mathematical and physical sciences. Specifically, the project will conduct research on four topics: the classification of affine and projective structures with...

This $118,647 Project Grant award from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049, Mathematical and Physical Sciences) supports fundamental research in descriptive set theory and its connections to other mathematical fields, including computability, operator algebras, topological dynamics, and ergodic theory. The award will fund research on questions related to amenability and hyperfiniteness, as well as investigations into classical geometrical paradoxes...

This federal Project Grant award for $300,000.00, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program, supports research to significantly expand the investigator's work on applications of model theory to the study of geometric structures. The key objectives are to: 1) tackle major transcendence problems such as the Ax-Lindemann-Weierstrass and Ax-Schanuel conjectures for uniformizing functions of geometric structures in higher...

The National Science Foundation's Division of Mathematical Sciences awarded $175,000 under the Mathematical and Physical Sciences program (CFDA 47.049) to the University of Georgia Research Foundation to support fundamental research in algebraic geometry. Effective August 1, 2025, through July 31, 2027, this project grant funds the Principal Investigator's research on the geometry and enumerative geometry of Kahler-Schüller-Bertin-Abramovich (KSBA) spaces, which generalize Deligne-Mumford moduli...

This $282,660 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research at The Ohio State University in the field of ergodic geometry. The project encompasses a research program on the long-term behavior of dynamical systems arising in geometry, particularly the geodesic flow which has important connections to the underlying space's geometry and topology. The principal investigator will pursue two main research...

This $160,457 Project Grant award from the National Science Foundation (NSF) Division of Mathematical Sciences supports research at Virginia Polytechnic Institute & State University (Virginia Tech) to establish new mathematical "structure theorems" for dynamical systems with multiple transformations. The project aims to advance the field of ergodic theory, which studies the long-term behavior of dynamical systems, by introducing a new framework for concatenation theory to derive...

This $1.2 million Project Grant from the National Science Foundation's Computer and Information Science and Engineering program will fund research into the fine-grained complexity of basic geometric problems from June 2022 through May 2025. The principal investigator at the University of Illinois will apply conditional proof techniques to establish new reductions between geometric optimization, searching, data structures, point cloud matching, and other problems. The goal is to prove conditional...

The National Science Foundation Division of Mathematical Sciences awarded $249,935 under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) to the University of California, Davis for a project grant titled "Questions in Algebraic and Geometric Combinatorics." The grant will support research into two areas of polytope theory from August 1, 2022 to July 31, 2025. The first part of the project focuses on studying Ehrhart positivity, valuations of polytopes, and...

This Project Grant award for $250,000 from the National Science Foundation (NSF) Division of Mathematical Sciences supports research on flat surfaces conducted by the Trustees of Boston College, a private nonprofit educational institution. The award, which runs from August 1, 2023 to July 31, 2026, focuses on advancing the understanding of flat surfaces and their applications across various fields, including geometry, dynamics, and algebraic structures. Through this project, the Principal...