Operator Algebras, Bi-Unitary Connections and Tensor Networks - Lecture 1

Explore the fascinating world of tensor categories and their role as a new form of "quantum symmetry" in this 1-hour 36-minute lecture by Yasuyuki Kawahigashi. Discover how tensor categories generalize classical group symmetry across various fields of mathematics and physics, including quantum groups, quantum topological invariants, quantum information, vertex operator algebras, conformal field theory, and topological order in condensed matter physics. Learn about the powerful Jones theory of subfactors in operator algebras and its application in studying these symmetries. Gain insights into bi-unitary connections as a tool for describing tensor categories using finite dimensional unitary matrices, with a particular focus on their relevance to tensor networks in 2-dimensional topological order. No prior knowledge of operator algebras is required to understand this comprehensive presentation.