This federal Project Grant award, valued at $145,144, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program. The award supports research at the University of Illinois in Chicago that aims to connect the fields of analysis, combinatorics, and model theory in mathematics. The primary goals are to develop a "fully general arithmetic regularity lemma" for arbitrary groups using continuous logic, and to provide a...
This $119,999 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports three main research projects centered around applications of model theory, a branch of mathematical logic. The first project aims to advance the use of model theory in solving differential and difference equations, which describe continuous and discrete dynamics, respectively. The second project focuses on developing connections between model...
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 National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) Project Grant award of $327,441 to the University of Illinois will fund research focused on challenges at the intersection of harmonic analysis, number theory, and dispersive equations. The principal investigator (PI) plans to explore connections between diverse mathematical fields, including additive combinatorics, classical Fourier analysis, dispersive equations on tori, and ergodic theory. The funded...
This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) will support research in descriptive set theory and computability at the University of California, Berkeley. The $170,000 award, spanning August 2024 to July 2027, will fund work in several areas: Studying questions on amenability and hyperfiniteness using tools from Gromov's theory of asymptotic dimension, with applications to topological dynamics and operator algebras. Research on...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research to develop a robust Scott analysis in the continuous setting, including applications, while also further applying and developing the Scott analysis in the more classical discrete setting. The $109,999 award, with a project period from September 1, 2025 to August 31, 2026, will be used by the University of Illinois to advance the mathematical...
The National Science Foundation Division of Mathematical Sciences awarded a $1,017,190 Project Grant to the University of Illinois under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The grant will support collaborative research on extremal combinatorics and flag algebras from August 1, 2022 to July 31, 2025. Specifically, the grant aims to resolve three prominent open questions in extremal combinatorics posed by Erdős, Turán, and Zarankiewicz using flag algebra...
This National Science Foundation (NSF) Project Grant Award, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $210,000.00 in funding to the University of Maryland, College Park to support research on the interplay between polylogarithms, cluster algebras, and hyperbolic geometry. The key objectives are to investigate key conjectures, find new examples of hyperbolic manifolds, and compute invariants using cluster coordinates. The project will involve both graduate and...
This Project Grant from the National Science Foundation Division of Mathematical Sciences provides $210,000 to Brandeis University under the Mathematical and Physical Sciences program (CFDA 47.049) from June 1, 2022 to May 31, 2025. The funding supports research in the field of combinatorics, which analyzes discrete data structures and is a central tool for solving problems in mathematics, computer science, and physics. Specific projects include unifying bijections between planar maps and...
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...