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This colloquium talk by Professor Alexei Davydov from Ohio University explores the evolution of mathematical symmetry concepts from traditional group theory to modern tensor categories. Discover how the limitations of group theory in explaining experimental developments in condensed matter physics during the late 20th century necessitated a broader mathematical framework for symmetry. Learn about the historical progression of group theory applications—from Galois' proof of quintic unsolvability to the classification of crystals in the 19th century and descriptions of matter states in the mid-20th century. The presentation introduces tensor categories as a generalized mathematical formulation of symmetry that addresses phenomena not captured by conventional group theory. Professor Davydov, who has worked at institutions including Moscow University, National University of Singapore, and Max Planck Institute before joining Ohio University, specializes in algebra, representation theory, and their connections to mathematical physics.
