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 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...
The National Science Foundation (NSF) awarded a Project Grant of $154,989 to Carnegie Mellon University under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award will fund research to deepen the interaction between combinatorics and algebraic geometry, including work on matroid theory, Coxeter combinatorics, and algebraic statistics. The project aims to reveal new structural properties of combinatorial objects and inform the complexity of maximum-likelihood...
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 award of $100,000.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports research in algebraic combinatorics, which investigates combinatorial structures arising in algebra and geometry. Specifically, the project aims to develop new combinatorial techniques in classical incidence geometry and further the theory and applications of cluster algebras. The research will involve...
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 Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), supports a research project on the interaction of algebra and geometry, with a focus on the resolution of singularities. The $209,771 award, effective August 15, 2024 through July 31, 2027, will fund research conducted by the University of Missouri System, exploring topics such as properties and applications of filtrations in local rings, inseparable local...
The National Science Foundation (NSF) awarded a $250,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to The Trustees of Princeton University Office of Research and Project Administration Division, doing business as Princeton University. This grant, awarded on June 1, 2024, will fund research centered on algebraic geometry and singularities in arithmetic settings, with the goal of developing new techniques to describe higher differential forms in positive...
This three-year, $611,884 project grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) supports collaborative research on higher categorical structures in algebraic geometry at Northwestern University from September 2022 through August 2025. The project aims to apply recent developments in higher category theory and condensed mathematics to longstanding questions in algebra and algebraic geometry relating to complete noncommutative categorical...