This National Science Foundation Project Grant of $250,000 supports research into low-dimensional topology through July 2025. Funded under the Mathematical and Physical Sciences program (CFDA 47.049), the award to Duke University will advance understanding of fundamental questions in knot theory and 4-manifold topology. Specifically, the principal investigator will investigate knot concordance problems tied to the unique properties of 4-dimensional manifolds compared to higher dimensions....
This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) provides $452,656 to California State University Fresno Foundation to support research in low-dimensional topology from September 1, 2022 to August 31, 2025. The funding will advance understanding of link homology theories and other quantum invariants through construction and study of new Khovanov-type homology theories for classical and singular knots. It will also investigate...
This $199,482 federal Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program supports research on the topology of 3-dimensional and 4-dimensional manifolds using tools from quantum field theory. The primary focus is on studying Floer homology for 3-manifolds with boundary and how it fits into an extended topological quantum field theory (TQFT). Key research areas include extending previous invariant work to manifolds...
This Project Grant from the National Science Foundation's $47.049 Mathematical and Physical Sciences program provides $294,584 to Virginia Commonwealth University from August 1, 2022 to July 31, 2025. The award supports research exploring knot theory and its applications to low-dimensional topology, as well as disseminating related knowledge. Specifically, the university will conduct fundamental investigations into knot invariants, crossing changes, tangle decompositions and unknotting...
This $177,469 Project Grant awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program supports research into the geometry of moduli spaces from low-dimensional topology and applications. The primary objectives are to study higher algebraic structures in instanton Floer homology, analyze the properties of generalized Seiberg-Witten equations, and explore applications of Kontsevich configuration space integrals in 4-dimensional topology....
Michigan State University was awarded a $436,377 project grant from the National Science Foundation Division of Mathematical Sciences on July 15, 2021 to complete work by June 30, 2024. The grant falls under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these fields and strengthen the nation's scientific enterprise through increased knowledge and understanding of major problems.
Specifically, the funding will support Michigan State...
Michigan State University was awarded a $377,544 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) to conduct research in topological quantum field theory and geometric structures in low dimensional topology from September 1, 2023 through August 31, 2026. Specifically, the university will study relations between quantum invariants and geometric structures in three-dimensional manifolds, investigate asymptotic aspects of...
The National Science Foundation (NSF) Division of Mathematical Sciences awarded a $153,765 Project Grant to Wayne State University from August 1, 2023 to July 31, 2026. This award, funded under the Mathematical and Physical Sciences program (CFDA 47.049), supports research focused on applications of equivariant stable homotopy theory - a central part of algebraic topology involving the study of topological objects and generalized cohomology theories.
The principal investigator will continue...
This $201,860 Project Grant awarded by the National Science Foundation (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) supports collaborative research focused on advancing the theories and applications of small quantum groups, their categorifications, and topological quantum field theories. The three-year grant, awarded on July 15, 2024, with a completion date of June 30, 2027, will engage students and postdocs, particularly those from...
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...