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 National Science Foundation Project Grant award in the amount of $241,311 provides funding from June 1, 2022 through May 31, 2025 to support research into arithmetic questions in the theory of linear algebraic groups at Michigan State University. The principal investigator will investigate the arithmetic, geometric, and structural aspects of algebraic groups over higher-dimensional fields, with a focus on various finiteness properties. Specific objectives include establishing finiteness...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) totaling $249,648 supports research on the relation between geometric and algebraic structures of groups. The award will fund the principal investigator's (PI) investigations into groups with geometric structures, focusing on situations where such groups have subgroups that exhibit undesirable geometric properties. Additionally, the PI will undertake efforts to broaden...
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 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 $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...
This $217,000 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences supports research on computational structures in equivariant chromatic homotopy theory, with a focus on developing new techniques to advance computations related to Lubin-Tate theories and the study of homotopy groups of spheres. The award funds a range of projects that leverage recent discoveries in equivariant homotopy theory to drive progress in chromatic homotopy theory and...
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 provides $169,979 to Haverford College under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) from June 2022 through May 2025. The award will support research addressing two topics in the algebra, geometry, and representation theory of reductive algebraic groups over non-Archimedean local fields. Specifically, the investigator will apply techniques from geometric group theory...
This Project Grant from the National Science Foundation's Division of Mathematical Sciences provides $194,999 to support collaborative research at Princeton University from June 2022 to June 2024. The funding falls under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and understanding in these fields. Specifically, the award will bring together researchers to address open problems at the intersection of matroids, graphs, and algebraic...