This two-year, $106,027 National Science Foundation Division of Mathematical Sciences Project Grant supports research into mapping class groups and transformation groups at the University of Maryland, College Park. The principal investigator and graduate students will develop new mathematical tools to study the structure of diffeomorphism groups and homeomorphism groups representing symmetries of manifolds. Previous work classified homomorphisms between such groups and proved conjectures...
The National Science Foundation awarded a $361,306 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to the University of Maryland, College Park for research titled "Geometries of Topological Groups." The three-year award beginning September 1, 2023 will support the university's efforts to solve open questions regarding the geometrization of topological groups through mathematical problems combining logic, analysis and metric geometry. As part of the...
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 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...
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 Division of Mathematical Sciences awarded a $165,663 Project Grant to the University of Maryland, College Park to support the research project "Coarse Geometry of Topological Groups" from November 1, 2021 through August 31, 2023. Under this award, the University of Maryland will conduct research into the coarse geometry of topological groups and deliver mathematical and computational products. The research is funded through the NSF's Mathematical and...
This $225,000 Project Grant awarded by the National Science Foundation's (NSF) Mathematical and Physical Sciences (MPS) program supports fundamental research in algebraic geometry. The grant aims to develop new tools in moduli theory and use them to advance the classification of algebraic varieties. This includes refining techniques for the deformation theory of stable pairs and analyzing wall-crossing phenomena for higher-dimensional moduli, with the goal of enabling progress in...
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) 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...
The National Science Foundation (NSF) awarded a $204,000 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the Regents of the University of Michigan to investigate rigidity phenomena in geometry and dynamics, with a focus on actions of higher rank abelian and semi-simple Lie groups and their lattices. This 3-year research project, with an award period from June 2024 to May 2027, will explore topics such as the classification of higher-rank...