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 $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 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 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 $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 $280,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research in birational geometry at New York University from April 2022 through March 2025. Specifically, the principal investigator will use methods from Galois cohomology of function fields, properties of algebraic cycles over non-algebraically closed fields, K-theory, and degeneration techniques to advance understanding of rationality and stable...
This is a $100,000 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The grant will support research by Virginia Commonwealth University (VCU) to investigate conformal field theories and their applications to the geometry of higher-dimensional algebraic varieties, as well as advancements in the theory of homological blocks for knots and 3-manifolds. The project aims to...
This $172,000 Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports research by Michigan State University on the birational classification of algebraic varieties. The key goals are to investigate the moduli theory and boundedness of Fano varieties over the integers, explore connections between birational geometry and commutative algebra/arithmetic geometry, and apply new techniques from derived algebraic geometry to study...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill (UNC) a $185,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports a three-year research project to develop Hodge theoretic techniques for studying Knizhnik-Zamolodchikov differential equations, which link representation theory, algebraic geometry, and mathematical physics. Key research activities include developing a...