Project Grant 2142656

This $180,139 National Science Foundation project grant supports collaborative research in enumerative algebraic geometry conducted by investigators at Rutgers, The State University. The research aims to resolve outstanding questions in enumerative geometry through the study of intersection theory on moduli spaces of geometric figures including flag varieties, their cotangent bundles, bow varieties, and Hessenberg varieties. Techniques include intersection theory, equivariant localization,...

This Project Grant award from the National Science Foundation Division of Mathematical Sciences, under the CFDA program Mathematical and Physical Sciences (47.049), provides $165,000.00 over 3 years from August 1, 2023 to July 31, 2026 to Texas A&M University for research in commutative algebra, algebraic geometry, and algebraic combinatorics. The primary focus of the research is using combinatorial models to understand affine varieties and the algebro-geometric significance of these models....

This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $162,825 to support collaborative research in enumerative algebraic geometry at Virginia Polytechnic Institute and State University from August 1, 2022 to July 31, 2025. The research aims to resolve outstanding questions in enumerative algebraic geometry through investigations of intersection theory in moduli spaces of geometric figures including flag varieties, their cotangent bundles, bow...

This $185,987 National Science Foundation Division of Mathematical Sciences Project Grant supports continued collaborative research in enumerative algebraic geometry at the University of North Carolina at Chapel Hill from August 1, 2022 through July 31, 2025. Specifically, the investigators and their graduate students will further their work resolving outstanding questions in enumerative algebraic geometry through techniques including intersection theory, equivariant localization, symmetric...

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 three-year Project Grant from the National Science Foundation Division of Mathematical Sciences, totaling $540,974, will fund collaborative research applying recent developments in higher category theory and condensed mathematics to longstanding questions in algebraic geometry and the introduction of new questions in analytic algebraic geometry. Specifically, the principal investigators and their collaborators at the University of California, Berkeley will pursue four main research...

This three-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program ($160,000) will support research at Michigan State University exploring the connections between cluster algebras, quantum groups, and decorated character varieties. The principal investigator will investigate the quantum geometry of moduli spaces within the framework of cluster algebras, examining relationships between decorated character varieties, quantum groups, and Legendrian...

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 collaborative research project, funded by the National Science Foundation's Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), was awarded $137,739 to the University of South Carolina on August 1, 2025, with a completion date of July 31, 2028. The project develops new mathematical tools and methods that bridge multigraded commutative algebra, toric geometry, and homological mirror symmetry by introducing symplectic geometry techniques...

This National Science Foundation project grant of $740,162 will fund collaborative research on extremal combinatorics and flag algebras from August 2022 through July 2025. The awardee is the University of Colorado Denver under the Mathematical and Physical Sciences program (CFDA 47.049). The research aims to resolve three prominent open questions in extremal combinatorics posed by Erdös, Turán, and Zarankiewicz using flag algebra techniques. The questions concern extremal hypergraph...