The National Science Foundation (NSF) Division of Mathematical Sciences awarded the University of North Carolina at Chapel Hill (UNC) a $185,000 Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports a three-year research project to develop Hodge theoretic techniques for studying Knizhnik-Zamolodchikov differential equations, which link representation theory, algebraic geometry, and mathematical physics. Key research activities include developing a motivic factorization formula for conformal block local systems, determining the structure of Hodge-Galois fusion rings, and computing examples of rigid local systems with finite global monodromy using Hodge theoretic criteria. The project aims to produce new insights relating these mathematical fields and their computational aspects, while also providing research training opportunities for graduate students.
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