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;...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $320,000 Project Grant to the University of Illinois, Urbana-Champaign under the Mathematical and Physical Sciences program (CFDA 47.049). The three-year grant, effective September 1, 2023 through August 31, 2026, supports fundamental research on symplectic groupoids and the quantization of Poisson manifolds. Key objectives include developing a novel non-formal deformation quantization approach, advancing the...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $399,773 Project Grant to the University of Illinois, Urbana-Champaign to support research on the "Interactions Between Geometry, Topology, Number Theory, and Dynamics" from August 1, 2023 to July 31, 2026. The research aims to advance the understanding of topology and geometry and their connections to other areas of mathematics and computer science, including applications in data mining and engineering...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a 3-year, $252,262 Project Grant to the University of Illinois to advance research in motivic homotopy theory. The project aims to develop tools for studying normed motivic spectra and computations of equivariant motivic invariants, with a focus on geometric applications. Broader impacts include work with incarcerated individuals and training of undergraduate and graduate students. This award supports NSF's mission...
The National Science Foundation awarded a $400,000 Project Grant to the University of Illinois under the Mathematical and Physical Sciences program (CFDA 47.049) from June 15, 2022 to May 31, 2025. The grant supports research into singularities in positive and mixed characteristic commutative algebra, advancing theoretical understanding and shedding light on problems in related fields. The Principal Investigator will investigate properties of the dual F-signature limit in characteristic P >...
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 National Science Foundation Project Grant of $400,000 will fund research into Bridgeland stability, moduli spaces, and their applications from July 2022 to June 2025. The awardee, the Board of Trustees of the University of Illinois, will utilize the funding under the Mathematical and Physical Sciences (47.049) program to advance the principal investigator's studies of moduli spaces of vector bundles and sheaves on surfaces. Through a novel technique called Bridgeland stability, the...
This National Science Foundation project grant of $102,612 supports research at the University of Illinois from October 1, 2022 through May 31, 2024 under the Mathematical and Physical Sciences program (CFDA 47.049). The award aims to advance understanding of dynamical systems and number theory through four objectives: developing methods in homogeneous dynamics to study rational points near manifolds and self-similar sets; techniques in random walk theory and representations of algebraic...
This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences program (CFDA 47.049) provides $199,482 to the University of Illinois for research on the topology of 3-manifolds and 4-manifolds using bordered Floer homology. The award period runs from August 15, 2024 to July 31, 2027. The key objectives of the research project are to: 1) extend invariants developed in the PI's previous work to 3-manifolds with multiple torus boundary components, and use...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $330,000 to the University of Illinois to conduct research on non-abelian Hodge theory and transcendence. The project aims to extend recent progress in classical Hodge theory and transcendence theory via o-minimal methods to the non-abelian setting. This includes addressing open questions related to the geometry of local systems on algebraic varieties and its...