Federal Project Grant Award Summary

The National Science Foundation's Division of Mathematical Sciences awarded University of California, Irvine $299,999 under the Mathematical and Physical Sciences (CFDA 47.049) program on August 15, 2026, for a research project extending through July 31, 2029. This project grant supports fundamental mathematical research on discrete approximation theory, analyzing functions of binary variables and their continuous analogues in discrete and Gaussian spaces. The principal investigator will develop a unified analytical program employing semigroup methods, Fourier analysis, hypercontractivity, and sharp inequalities to advance understanding of function approximation, learning complexity, and high-dimensional geometry with applications to machine learning, quantum computing, and data science.

The research deliverables include the development of sharper Bohnenblust-Hille and hypercontractive inequalities applicable to Probably Approximately Correct (PAC) learning, polynomial threshold functions, and quantum query complexity; Jackson- and Poincaré-type approximation theorems with dimension-independent bounds; and advances on isoperimetric and influence inequalities including progress toward resolving the Kahn-Park Conjecture. The grant also supports workforce development through training of graduate students and postdoctoral researchers, research programs for early-career scientists, and dissemination of findings via seminars, webinars, and preprints to strengthen the mathematical sciences workforce and advance the nation's computational and artificial intelligence capabilities.