This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $299,996 to Utah State University (USU) from August 2024 to July 2027 to conduct research on developing new algebraic and geometric tools for formulating quantum physics concepts in precise mathematical terms.
The key focus areas include investigating "re-normalized quantum invariants" from non-semi-simple categories to interpret topological quantum field theories, as well as enhancing and generalizing recently defined non-compact skein topological quantum field theories. The research aims to further explore the nature and physical significance of these mathematical frameworks, particularly in the context of Chern-Simons theory and vertex operator algebras. The broader impacts involve STEM education, mentoring, and outreach activities to foster collaborative research and applications of this work.
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