The University of Utah Office of Sponsored Projects Division was awarded a $330,000 Project Grant from the National Science Foundation Division of Mathematical Sciences under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will fund research in the field of algebraic geometry from July 2023 to June 2026. Specifically, the Principal Investigator will generalize results from the Minimal Model Program over complex numbers to varieties over algebraically...
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 $285,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Utah to conduct research on hyperbolic geometry in two- and three-dimensional spaces. The project, running from August 1, 2024 to July 31, 2027, will focus on studying the geometry of hyperbolic 3-manifolds, including investigating the renormalized volume of such manifolds and the connection to the Weil-Petersson gradient flow. The...
This $204,372 federal Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) supports research on the potential theoretic aspects of complex geometry. The principal investigator will employ methods from potential theory, infinite-dimensional geometry, and geometric analysis to investigate a cluster of interconnected questions and conjectures in complex geometry. The project aims to advance scientific knowledge in this...
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 $225,000 National Science Foundation Project Grant supports research in algebraic geometry at the University of Georgia Research Foundation from July 2022 through June 2025. The Mathematical and Physical Sciences program aims to increase scientific knowledge and understanding in major problems through support of basic research. Specifically, this award will fund the principal investigator's research on degenerations of algebraic varieties and geometric compactifications of moduli spaces...
The National Science Foundation awarded a $201,000 Project Grant to the University of California, Berkeley under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research in Diophantine geometry and arithmetic geometry, which study solutions to families of polynomial equations. Specifically, the principal investigator and collaborators will develop new frameworks to prove the irrationality of certain conjectured numbers through analysis of rational...
This Project Grant award, valued at $250,000.00, was provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program to Brown University. The primary focus of this 3-year project is to conduct research in the areas of moduli theory and birational geometry within the field of algebraic geometry, which has important applications in coding, industrial control, computation, and theoretical physics. Key research activities include studying the...
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 $178,637 Project Grant awarded by the National Science Foundation's Division of Mathematical Sciences on July 15, 2023 supports research on K-stability and moduli spaces of higher dimensional algebraic varieties at Northwestern University. The Principal Investigator will study canonical geometric structures known as Einstein metrics to address the fundamental moduli problem in algebraic geometry. Key research objectives include constructing compact moduli spaces of K-unstable Fano...