Project Grant 2152095
- 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....
- This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $231,902 to East Carolina University to support collaborative research on definability and computability over arithmetically significant fields from July 15, 2022 to June 30, 2025. The research will consider several problems at the intersection of number theory, algebraic geometry, model theory, computability theory, and...
- The National Science Foundation Division of Mathematical Sciences awarded a $141,400 Project Grant to the University of Illinois under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support research into Galois structures and arithmetic statistics in number theory from August 15, 2022 to July 31, 2025. Specifically, the principal investigator and collaborators will modify non-abelian Cohen-Lenstra heuristics when the base field contains roots of unity;...
- 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...
- The National Science Foundation (NSF) awarded a $405,500 Project Grant under its Mathematical and Physical Sciences (CFDA 47.049) program to Duke University to support a research program in A1-homotopy theory and its applications to enumerative geometry and number theory. The award will fund research to develop enriched counting methods that can detect differences in the number of solutions to equations requiring real or imaginary numbers, with potential applications in number theory and...
- 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 $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 federal Project Grant award for $300,000.00, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program, supports research to significantly expand the investigator's work on applications of model theory to the study of geometric structures. The key objectives are to: 1) tackle major transcendence problems such as the Ax-Lindemann-Weierstrass and Ax-Schanuel conjectures for uniformizing functions of geometric structures in higher...
- This $150,000 Project Grant, awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA 47.049), supports collaborative mathematical research conducted at Temple University from August 1, 2025 through July 31, 2027. The project delivers fundamental mathematical research and scholarship at the interface of geometry, topology, algebraic geometry, number theory, and dynamics, with particular emphasis on real and...
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 the intersection of logic, number theory, algebraic geometry, model theory, computability theory and valuation theory as they relate to polynomial equations. Specific areas of focus include extending Hilbert's Tenth Problem to fields of rational numbers and rings of algebraic integers, and studying definability and computability in the first-order language of rings over number fields, rings of integers, and their infinite algebraic extensions. Insights gained will also contribute to related open problems in function fields and rings of all characteristics. The work involves graduate student training and development of an online collaboration platform to facilitate interaction across mathematics disciplines studying these critically important problems.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $220.2k | 7/13/22 |