This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research into combinatorial algebraic geometry, including the study of flag varieties, toric geometry, and applications. The $121,201 award from January 1, 2025 to June 30, 2027 will fund research objectives such as advancing the theory of combinatorial subvarieties of the flag variety, proposing a notion of duality for Newton-Okounkov bodies, and studying...
This $210,000 Project Grant awarded by the National Science Foundation Division of Mathematical Sciences under the CFDA Program 47.049 "Mathematical and Physical Sciences" will fund research in algebraic combinatorics and braid varieties. The project aims to use algebraic methods to produce new combinatorial results with applications in areas like cryptography, protein folding, high-energy physics, and quantum computing. Specifically, the funds will support exploring the use of braid...
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 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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will fund research at Arizona State University (ASU) focused on advancing the field of commutative algebra. The $225,000 award, effective August 15, 2024 through July 31, 2027, will support investigations into multigraded commutative algebra and the asymptotic behavior of filtrations of ideals. The project aims to enhance the understanding of Hilbert series, explore...
This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $205,601 to the University of Massachusetts for research related to enumerative, algebraic, and asymptotic combinatorics with connections to representation theory and geometry. Specifically, the award supports three research projects that will study problems in graph colorings, Schubert polynomials, and integer flows on graphs...
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...
This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) will support fundamental research by Brigham Young University in the field of algebraic geometry. The key goals of the $125,000 award, with a performance period from July 15, 2025 to June 30, 2027, are to: Understand the motivic Euler characteristic, a crucial algebraic geometry invariant, for Hilbert schemes of K3 surfaces, including characterizing its...
This Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research in commutative algebra and algebraic geometry. The $207,142 award to Oberlin College will fund investigations into several classical algebraic structures, including differential operators, almost complete intersections, and Gorenstein ideals. The project aims to develop new homological techniques to understand the geometric...
This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences program (CFDA 47.049) provides $210,000 in funding to The Trustees of Smith College to support research on combinatorial models in representation theory, geometry, and analysis. The key focus areas of the research project include optimizing and analyzing two types of edge-labeled graphs: webs from knot theory and representation theory, and algebraic splines from applied mathematics. The...