This National Science Foundation (NSF) Project Grant, awarded under the Mathematical and Physical Sciences program (CFDA 47.049), provides $172,247 to support collaborative research on small quantum groups, their categorifications, and topological applications. The research aims to bridge the gap between 3D topological quantum field theories and our 4D universe, with a focus on developing homological invariants of 3D and 4D manifolds. The project will involve students and postdocs,...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports fundamental research on graph theory and its applications. The award of $150,000.00 to the Georgia Tech Research Corporation, which will run from August 1, 2025 to July 31, 2028, focuses on developing structural techniques for understanding dense graphs. Key areas of focus include forbidding vertex-minors and studying graphs with a dependent first-order...
This National Science Foundation Project Grant award of $472,476 provides funding from July 1, 2022 through June 30, 2025 to support research into variational questions in mathematics and physics. The award is made under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to advance scientific knowledge and understanding of major problems. The principal investigator will pursue research questions related to optimal states and equilibrium conditions in quantum mechanical...
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 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 $299,996 Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences under the Mathematical and Physical Sciences (CFDA 47.049) program supports fundamental mathematical research by a team at Utah State University. The project aims to develop new algebraic and geometric tools to formalize and advance the mathematical theory underlying quantum physics, particularly in low-dimensional topology and the theory of quantum invariants. The key products and...
This federal Project Grant award in the amount of $177,469.00 was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences Grant Program (CFDA #47.049). The award will support research into the geometry of moduli spaces from low-dimensional topology and applications, with a focus on three main directions: studying higher algebraic structures in instanton Floer homology, analyzing the properties of generalized Seiberg-Witten equations, and exploring the...
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....
The National Science Foundation Division of Mathematical Sciences awarded a $389,346 Project Grant to the Georgia TECH Research Corporation for research titled "Topology Between Dimensions Three and Four." The award period is from June 1, 2021 through May 31, 2024. The grant is part of the NSF's Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in these fields and strengthen the nation's scientific enterprise through increasing knowledge and...
This $330,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program supports research into quantum groups, W-algebras, and Brauer-Kauffmann categories, with a focus on understanding the underlying mathematical symmetries that govern natural phenomena. The principal investigator will develop emerging theories and applications of I-quantum groups, including exploring braid group actions, Drinfeld presentations, and...