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...
This National Science Foundation (NSF) Mathematical and Physical Sciences (CFDA 47.049) project grant award of $200,000 to North Carolina State University (NC State) will support research in geometric topology, knots, and four-dimensional manifolds. The primary investigator will develop tools to measure the complexity of these mathematical structures, construct new exotic four-manifolds, and study surfaces in four-manifolds, including finding exotic embeddings and non-orientable surfaces. The...
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 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program, CFDA 47.049, will support research into the use of algebraic invariants and Floer homology to study the topology of three-dimensional spaces and knots. The $200,000 award to the Georgia Tech Research Corporation will fund projects that aim to provide a simpler characterization of when high-dimensional topological manifolds are triangulable, as well as investigate properties of...
This National Science Foundation Project Grant award of $104,011 provides funding from July 1, 2022 through June 30, 2024 to support research in differential topology at Rutgers University-Newark. The award is made under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in mathematics and the physical sciences. Specifically, the funding will support research into complex plane curves and their applications in 4-dimensional topology. The principal...
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 National Science Foundation (NSF) Division of Mathematical Sciences Project Grant for $281,433 awarded to Claremont McKenna College supports research in pure and applied knot theory. The project aims to connect quantum topology with hyperbolic geometry and apply knot theory techniques to the study of knotted biopolymers. Key research focus areas include: Investigating how quantum invariants of knots relate to the geometric properties of knots and 3-dimensional spaces, with potential...
This Project Grant award of $317,407 from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will support research at the University of Nebraska on the topology of 3- and 4-dimensional manifolds. The project aims to uncover deep connections between manifold theory in these dimensions, with potential applications in fields such as biology, chemistry, physics, and quantum computing. Specific objectives include proving additional cases of the Smooth...
This $200,000 National Science Foundation project grant supports mathematical and physical sciences research at Michigan State University from September 2022 through August 2025. The award falls under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and address national problems through basic research and education in these fields. Specifically, the principal investigator and their team will investigate Floer and Khovanov theories...
This Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports fundamental research into the topology and dynamics of four-dimensional manifolds with symplectic structures. The $156,571 award, spanning from September 1, 2024 to August 31, 2026, will enable the principal investigator to employ advanced mathematical tools, such as surgery on Lefschetz fibrations, Gromov-Witten theory, and family...