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 Division of Mathematical Sciences awarded $220,150 under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to support collaborative research on definability and computability over arithmetically significant fields. The George Washington University will lead the project in partnership with other institutions. The award period is from July 15, 2022 through June 30, 2025. The project aims to advance understanding of fundamental questions at...
This National Science Foundation project grant award of $171,147 provides funding from July 2022 through June 2025 to support collaborative research on definability and computability over arithmetically significant fields at the University of California, Irvine. The research will consider several problems at the intersection of number theory, algebraic geometry, model theory, computability theory and valuation theory regarding definability and computability over number fields, rings of integers,...
This National Science Foundation Project Grant award of $222,314 supports collaborative research on definability and computability over arithmetically significant fields at The Ohio State University from July 2022 through June 2025. The research will consider several problems in definability and computability over fields important to number theory, algebraic geometry, model theory, computability theory and valuation theory. Specifically, the principal investigators intend to study...
This $290,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports research in computable model theory and invariant descriptive computability theory. The award, spanning July 2024 to June 2027, will fund work that explores connections between computability theory and the fields of model theory and set theory within mathematical logic. Key objectives include investigating cases where mathematically equivalent objects have...
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 $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 $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 $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 $186,112 project grant, awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research at the interface of algebraic geometry, string theory, and quantum field theory. The project aims to explore major open problems at this intersection, employing techniques from fields such as topology, integrable systems, and supergeometry. Specific research topics include investigating the Geometric Langlands...