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...
The National Science Foundation Division of Mathematical Sciences awarded a $389,346 Project Grant to the Georgia TECH Research Corporation for research titled "Topology Between Dimensions Three and Four." The award period is from June 1, 2021 through May 31, 2024. The grant is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these fields and strengthen the nation's scientific enterprise through increasing knowledge and...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) provides $137,633 to the University of Chicago to investigate the connections between non-Euclidean hyperbolic geometry and Euclidean geometry. The research aims to develop a stronger link between the earthquake and horocycle flows, study the structure of optimal Lipschitz maps between hyperbolic surfaces, and investigate related counting problems on flat and...
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...
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...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports a research and training program at the University of California, Irvine (UC Irvine). The $998,809 award will fund a series of improvements and new additions to UC Irvine's undergraduate, graduate, and postdoctoral training programs in geometry and topology, which have applications in mathematical physics, data science, and video game design. The projects aim to...
The National Science Foundation (NSF) awarded a $112,949 Project Grant to The Trustees of the Stevens Institute of Technology to conduct research under the Mathematical and Physical Sciences (CFDA 47.049) program. The project, titled "Uniformization of Surfaces and Mapping Problems in Metric Spaces", aims to develop new mathematical approaches for understanding the geometry of non-smooth spaces, building on the classical Uniformization Theorem. The research will investigate methods for...
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 $170,443 Project Grant to the University of Massachusetts Boston (UMass Boston) under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research in "Critical Symplectic Geometry, Lagrangian Cobordisms, and Stable Homotopy Theory." The project aims to incorporate ideas from homotopy theory and category theory into symplectic geometry to prove structural results about...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $400,000 Project Grant to New York University (NYU) for the period of August 1, 2023 to July 31, 2026. The grant, funded under the Mathematical and Physical Sciences program (CFDA 47.049), focuses on two key areas: Studying geometric evolution equations, specifically mean curvature flow and Ricci flow, with a focus on different aspects of regularity. This research aims to address longstanding open problems at the...