Fixed-Point-Free Fusion Automorphisms in Quantum Symmetry

Learn about fixed-point-free fusion automorphisms in this 59-minute lecture from the BIMSA-Tsinghua Quantum Symmetry Seminar featuring Andrew Schopieray from the University of Alberta. Explore how symmetries in algebraic objects can reduce complexity, particularly when there are fewer fixed points. Discover the implications of fixed-point-free symmetries, where only the unit or neutral element remains fixed, and examine their applications in finite groups, fusion rings, and categories. Understand classical results about fixed-point-free automorphisms of finite groups and their potential generalization to fusion rings and categories, with special attention to when combinatorial symmetries of fusion rings can be elevated to categorical symmetries of fusion categories. Benefit from a self-contained presentation aimed at a general audience, complete with numerous examples to illustrate key concepts. The speaker, who transitioned from professional cooking to mathematics, brings diverse academic experience from institutions across the United States, Australia, and Canada, combining expertise in tensor categories with a passion for alpine climbing and wildlife photography.