The National Science Foundation (NSF) awarded a 5-year, $304,875 CAREER grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Notre Dame. The grant will support a research program at the interface of algebraic geometry and topology, focused on better understanding the structure and asphericality (vanishing of higher homotopy) of moduli spaces. The project aims to develop new methods using topology and geometric group theory to study strata of abelian...
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...
This Project Grant from the National Science Foundation's Division of Mathematical Sciences provides $169,979 to Haverford College under the Mathematical and Physical Sciences federal grant program (CFDA 47.049) from June 2022 through May 2025. The award will support research addressing two topics in the algebra, geometry, and representation theory of reductive algebraic groups over non-Archimedean local fields. Specifically, the investigator will apply techniques from geometric group theory...
This $249,648 federal Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support research by Tufts University to investigate the relationship between the geometric and algebraic properties of groups. The project aims to understand the boundary structure and subgroup behavior of hyperbolic and relatively hyperbolic groups, which have applications in cryptography and algorithms. In addition, the award will fund initiatives...
The University of Notre Dame received a $104,070 Project Grant award from the National Science Foundation Division of Mathematical Sciences. The grant period runs from October 1, 2021 to June 30, 2023 to support research related to the MONODROMY IN TOPOLOGY AND GEOMETRIC GROUP THEORY project under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The Mathematical and Physical Sciences program aims to promote progress in these fields and strengthen the nation's...
This National Science Foundation award under the Mathematical and Physical Sciences program (CFDA 47.049) provides $275,396 to the University of Oklahoma from August 1, 2023 through July 31, 2026. The funding supports research into the geometries and topologies of surfaces and graphs. Specifically, the award will advance understanding of how abstract algebraic groups manifest as symmetries of geometric spaces in one and two dimensions. Graduate students will gain research experience applying...
This federal Project Grant award from the National Science Foundation (NSF) Integrative Activities (IA) program totaling $147,973 will support research to study Coxeter and hyperbolic groups from the perspective of geometric group theory. Key activities will include developing new quasi-isometry invariants, investigating the rigidity properties of Coxeter groups, and exploring the subgroup structure of hyperbolic groups. The project aims to advance fundamental understanding of these prominent...
This $105,981 project grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental research at the intersection of number theory, representation theory, and geometry. The research aims to explore geometric techniques in representation theory, with a focus on connections between representations of reductive algebraic groups over local fields and geometric constructions like...
The National Science Foundation awarded Indiana University a $142,059 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct research investigating ways to characterize, describe, and study spaces with many symmetries in various dynamical, geometric, and topological settings. The grant will support research exploiting connections between a wide range of mathematical areas to further understand fundamental structures related to lattices in Lie groups. Key...
This three-year Project Grant from the National Science Foundation's Mathematical and Physical Sciences program, totaling $215,864, will fund research into low-dimensional topology through August 2025. Specifically, the principal investigator at the University of Notre Dame will employ combinatorial tools to study problems involving knots, surfaces embedded in four-dimensional manifolds, and the detection of exotic smooth structures in dimension four. This includes investigating the meridional...