Project Grant 1906441

The National Science Foundation (NSF) awarded a $285,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Utah to conduct research on hyperbolic geometry in two- and three-dimensional spaces. The project, running from August 1, 2024 to July 31, 2027, will focus on studying the geometry of hyperbolic 3-manifolds, including investigating the renormalized volume of such manifolds and the connection to the Weil-Petersson gradient flow. The...

This Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $211,013 to Wesleyan University to support research into rigidity and boundaries in non-positive curvature geometry. The Principal Investigator will investigate asymptotic invariants and rigidity phenomena for finitely generated groups and their large-scale geometry. This includes studying graphical discreteness to unify notions...

This three-year $215,251 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research at the University of Tennessee to develop techniques in the field of analysis on metric spaces and geometric measure theory. The goals of the research are to relate integral bounds for discrete forms of curvature on non-smooth manifolds with locally Euclidean bi-Lipschitz parameterizations in dimensions greater than or equal to three,...

The National Science Foundation (NSF) Division of Mathematical Sciences awarded a 3-year, $250,000 Project Grant to the University of Wisconsin - Madison under the Mathematical and Physical Sciences program (CFDA 47.049) to investigate moduli spaces of surfaces with additional geometric structure. The grant will fund research to solve long-standing conjectures about the geometry and topology of these moduli spaces, which are mathematical spaces that parameterize the shapes an object can take....

This three-year project grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $349,952, will support research into the curvature of four-dimensional manifolds at Stony Brook University from September 2022 through August 2025. Specifically, the principal investigator will investigate generalizations of Einstein's field equations of general relativity in the Riemannian setting without distinguishing between space and time. The research aims to...

This three-year National Science Foundation Project Grant of $378,000 will support research into boundaries of groups in geometric group theory and hyperbolic geometry at the University of Illinois at Chicago from September 2022 through August 2025. Specifically, the principal investigator and collaborators will investigate the Cannon Conjecture regarding differences between classical and Gromov hyperbolic geometry in three dimensions in the presence of symmetries. They will continue...

This three-year $350,000 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program will support research at the University of Maryland, College Park on moduli spaces of Higgs bundles, gauge theory, and related topics in complex geometry. The principal investigator will further studies on moduli spaces of Higgs bundles on Riemann surfaces, including work on parabolic lambda-connections, construction of a universal moduli space, and the asymptotic and...

This Project Grant award from the National Science Foundation (CFDA 47.049 - Mathematical and Physical Sciences) to Northeastern University totals $243,319 over the period from August 1, 2023 to July 31, 2026. The project will use effective techniques in geometric microlocal analysis to study singular metrics and address problems related to metric degenerations, including perturbation theory, singular uniformization problems, parametrization of moduli spaces, and related geometric properties....

This three-year, $168,974 National Science Foundation Mathematical and Physical Sciences project grant funds research at Princeton University to advance understanding of smooth structures in four-dimensional manifolds. Specifically, the grantee aims to (1) classify smooth four-manifolds up to stable diffeomorphism by connected sum with S^2 x S^2, (2) characterize smooth structures on topological four-balls embedded in S^4, and (3) study embeddings of contractible manifolds called...

This Project Grant award for $330,586, provided by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences program (CFDA No. 47.049), supports research on the geometric and metric properties of two-dimensional surfaces. The principal investigator (PI) at Cornell University will investigate the classification of surfaces under singular flat and hyperbolic metrics, as well as the associated moduli spaces and related mathematical...