Project Grant 2154459

This Project Grant from the National Science Foundation Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), provides $261,101 to the University of Delaware to conduct research on noncommutative analysis in the theory of nonlocal games from July 1, 2022 to June 30, 2025. The project aims to further the links between combinatorial and probabilistic nonlocal games and mathematical analysis on noncommutative structures. It will contribute to the current large-scale quantization program in mathematics by studying the passage from classical to quantum nonlocal games. The work will enhance interdisciplinarity in pure mathematics while supporting national quantum initiatives. Key objectives include identifying quantum versions of graph isomorphism games and characterizing their perfect strategies using operator theory, developing operator algebraic methods of strategy transfer between games, and providing closed formulas for optimal quantum game winning probabilities using operator tensor norms. The research employs techniques such as operator theory, completely bounded maps, tensor theory for operator algebras, and von Neumann algebra theory. Broader impacts include training undergraduate and graduate students.