This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $144,469 to the University of Washington from February 1, 2023 through July 31, 2024. The grant supports research exploring connections between equivariant and chromatic homotopy theory to produce computations in chromatic homotopy theory. Specifically, the Principal Investigator will study periodicity phenomena in the stable...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $153,765 Project Grant to Wayne State University from August 1, 2023 to July 31, 2026. This award, funded under the Mathematical and Physical Sciences program (CFDA 47.049), supports research focused on applications of equivariant stable homotopy theory - a central part of algebraic topology involving the study of topological objects and generalized cohomology theories. The principal investigator will continue...
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 Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research related to chromatic homotopy theory, algebraic K-theory, and L-functions. The $182,359 award to Trustees of Indiana University, doing business as Indiana University, aims to further explore the connections between number theory and homotopy theory. The research will investigate generalizations of the Quillen-Lichtenbaum conjecture, the multiplicative...
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...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a 3-year, $252,262 Project Grant to the University of Illinois to advance research in motivic homotopy theory. The project aims to develop tools for studying normed motivic spectra and computations of equivariant motivic invariants, with a focus on geometric applications. Broader impacts include work with incarcerated individuals and training of undergraduate and graduate students. This award supports NSF's mission...
The National Science Foundation (NSF), through its Integrative Activities program (CFDA 47.083), has awarded a $153,804 project grant to New Mexico State University (NMSU) for the period of July 1, 2023 to June 30, 2026. The grant will fund research by NMSU to advance equivariant homotopy theory, a field that studies the symmetries of geometric shapes. Key objectives include developing generalized Steenrod operations and equivariant analogs of Stiefel-Whitney classes, which have applications...
This National Science Foundation Project Grant award of $282,638 provides funding from June 1, 2022 to May 31, 2025 to support research in commutative and homological algebra at the University of Nebraska. Specifically, the award will further investigations into open conjectures regarding the possible values of Euler characteristics of certain complex structures and lengths of modules of finite projective dimension. The research project involves four main topics: establishing bounds on module...
This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) project grant award of $106,619 to Case Western Reserve University supports fundamental research in classical and motivic stable homotopy theory, a field of algebraic topology. The key projects involve computing homotopy groups of spheres, including leveraging computer calculations to overcome technical challenges, as well as exploring analogues of these groups in algebraic geometry through motivic homotopy...
This National Science Foundation (NSF) Project Grant award, under the Mathematical and Physical Sciences program (CFDA 47.049), will support research on the factorization and degeneration of chiral homology, a fundamental area of mathematics with applications in physics, engineering, and the arts. The $199,927 award to the University of Texas at Austin, spanning from August 2024 to July 2027, will fund research to understand how chiral homology, which encodes the symmetries of certain...