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...
The National Science Foundation (NSF) awarded a $240,000 Project Grant to Lebanon Valley College under the agency's Mathematical and Physical Sciences program (CFDA 47.049) to study theoretical problems in physics and mathematics related to quantum advantage. The 3-year grant supports implementation of a resource theory framework to analyze invertible free operations, including local unitary transformations, permutations of subsystems, and matchgates, in order to probe multiparticle quantum...
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...
The National Science Foundation (NSF) Division of Physics awarded a $137,548 Project Grant to the University of New Mexico (UNM) under the Mathematical and Physical Sciences program (CFDA 47.049). The 3-year grant, running from September 1, 2023 to August 31, 2026, will fund research to deepen the understanding of quantum computational advantage. Specifically, the project seeks to explore the interplay between entanglement, measurement, and quantum many-body physics in the context of "noisy...
The National Science Foundation (NSF) awarded a $180,000 Project Grant to the University of Southern California (USC) Department of Contracts and Grants Division under the Mathematical and Physical Sciences (CFDA 47.049) program. The 3-year grant will support research on "Combinatorial Representation Theory of Quantum Groups and Coinvariant Algebras." The project aims to further develop combinatorial diagrams called "web bases" that encode the representation category of...
This $340,000 collaborative research project, awarded by the National Science Foundation (NSF) under the Mathematical and Physical Sciences program (CFDA 47.049), supports professors at the City College of the City University of New York and Lehman College in advancing the understanding of fundamental physical phenomena like quantum entanglement and the relationship between gravity and the curvature of space and time. The research will utilize mathematical tools from geometry, abstract...
The National Science Foundation (NSF) awarded a $343,286 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Oregon. The three-year grant, starting on August 1, 2024, supports research on C*-algebras and dynamics beyond the Elliott classification program. The key objectives are to investigate when simple C*-algebras, a type of mathematical object with applications in quantum mechanics, are isomorphic to their opposite algebras. The project aims...
The National Science Foundation (NSF) Division of Materials Research awarded a $387,177 Project Grant to Florida State University (FSU) under the Mathematical and Physical Sciences Program (CFDA 47.049) to support theoretical research and education on exotic quantum phases of many-particle systems with strong interactions. The key products and services to be delivered through this 3-year grant include: Theoretical studies of the physical properties of the edges and interfaces separating...
The National Science Foundation (NSF) awarded a $240,000 CAREER grant to The Trustees of Columbia University in the City of New York to support theoretical research and educational activities in the rapidly evolving field of quantum materials. The project, funded through the NSF's Mathematical and Physical Sciences (CFDA 47.049) program, aims to study how the quantum geometry of electron wavefunctions affects the collective properties of electrons in both clean and disordered quantum...
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,...