Project Grant FA86552517469

This $451,324 National Science Foundation Project Grant supports collaborative research on definability and computability over arithmetically significant fields through The Trustees of the University of Pennsylvania. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), this three-year award will advance understanding of polynomial equations, a foundational mathematical language, through interaction of logic, number theory, algebraic geometry, topology and related areas....

The National Science Foundation (NSF) awarded a 3-year, $155,000 Project Grant under the Integrative Activities (CFDA 47.083) program to the Board of Regents of the University of Nebraska, doing business as the University of Nebraska, for research in commutative algebra and algebraic geometry. The project focuses on three areas: symbolic powers of ideals and higher-order polynomial interpolation, homological properties of symmetric ideals, and the algebraic Lefschetz property. The research...

This $200,000 National Science Foundation Division of Mathematical Sciences Project Grant will support research and training in noncommutative algebra and geometry at the University of California Irvine from July 1, 2022 to June 30, 2025. The award will advance fundamental understanding of noncommutative algebraic structures that arise in geometry and physics. Researchers will develop new techniques to deduce good algebraic properties for geometrically constructed noncommutative algebras and...

This Project Grant award, funded by the National Science Foundation's STEM Education program (CFDA 47.076), aims to gain deeper insights into how undergraduate students in computer science and mathematics approach and comprehend fundamental discrete mathematics concepts. The $175,000 award to the California State University Long Beach Research Foundation will span one academic year from August 2024 to July 2025. The project will utilize a novel analytical approach combining the frameworks of...

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 $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 $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 $300,000 Project Grant award from the National Science Foundation (NSF) under the Computer and Information Science and Engineering (CFDA 47.070) program supports collaborative research at North Carolina State University (NC State) to develop new algorithmic approaches for efficiently and rigorously computing real solutions to systems of nonlinear polynomial equations. The project aims to advance both the mathematical theory and computational methods for solving such equations, which are...

This $260,000 Project Grant awarded by the National Science Foundation's (NSF) Division of Mathematical Sciences aims to advance the understanding of algebraic points on mathematical varieties. The primary research focus is on characterizing the arithmetic and local properties of algebraic points on curves, with complementary projects exploring higher dimensional varieties such as surfaces. The award also supports mentoring and training of early career mathematicians, particularly from...