Project Grant 2452236
- This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) is focused on three distinct problems in number theory, combinatorics, and ergodic theory. The $184,738 award will support research on generalizations of Szemerédi's Theorem, which concerns the existence of long arithmetic progressions in sufficiently large sets of integers. The investigator will also study the size and structure of integer distance sets. Additionally, the...
- This Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $261,101 to the University of Delaware to conduct research on noncommutative analysis in the theory of nonlocal games from July 1, 2022 to June 30, 2025. The project aims to further the links between combinatorial and probabilistic nonlocal games and mathematical analysis on noncommutative structures. It will contribute to the...
- This $118,647 Project Grant award from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049, Mathematical and Physical Sciences) supports fundamental research in descriptive set theory and its connections to other mathematical fields, including computability, operator algebras, topological dynamics, and ergodic theory. The award will fund research on questions related to amenability and hyperfiniteness, as well as investigations into classical geometrical paradoxes...
- 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 Project Grant from the National Science Foundation's Division of Mathematical Sciences provides $169,979 to Haverford College under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) from June 2022 through May 2025. The award will support research addressing two topics in the algebra, geometry, and representation theory of reductive algebraic groups over non-Archimedean local fields. Specifically, the investigator will apply techniques from geometric group theory...
- 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 $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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) totaling $249,648 supports research on the relation between geometric and algebraic structures of groups. The award will fund the principal investigator's (PI) investigations into groups with geometric structures, focusing on situations where such groups have subgroups that exhibit undesirable geometric properties. Additionally, the PI will undertake efforts to broaden...
- This $150,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on two open problems in algebraic combinatorics that intersect representation theory and algebraic geometry. The principal investigator and collaborators aim to use combinatorics to better understand these abstract mathematical objects in a more concrete way, with potential applications in mathematics, physics, and human-machine...
- This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049) provides funding of $238,061 to the University of Delaware from August 15, 2024 to July 31, 2027. The award supports the Principal Investigator's research to develop a systematic mathematical approach for analyzing and visualizing large complex networks, such as social networks, biological networks, and neural cell networks. The key research objectives include...
This $203,650 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Federal Grant Program (CFDA 47.049) supports research on difference sets and partial difference sets, which are mathematical objects with strong regularity that have wide-ranging applications in areas such as finite geometry, coding theory, and information security. The research, conducted by the University of Delaware, aims to uncover novel constructions of these difference sets and partial difference sets, with the goal of advancing the constructive landscape in this field. Specifically, the project will focus on three key directions: (1) constructing difference sets in abelian groups with high exponents, (2) generalizing classical Denniston partial difference sets to a wider range of parameters and groups, and (3) advancing construction techniques beyond abelian settings to nonabelian groups. The project is expected to be completed by August 31, 2028.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $203.7k | 7/31/25 |