Operator Algebras, Tensor Categories and Tensor Networks in Topological Order

Explore the intersection of operator algebras, tensor categories, and tensor networks in this lecture on quantum symmetries and two-dimensional topological order in condensed matter physics. Delve into the application of operator algebra techniques, particularly the Jones theory of subfactors, to study tensor category structures. Discover how bi-unitary connections, a form of generalized quantum 6j-symbols, serve as powerful finite-dimensional tools for analyzing these structures. Examine various applications in the theory of two-dimensional topological order and their relevance to mathematical theories of topological quantum computations. Gain insights into how these advanced mathematical concepts contribute to our understanding of new symmetries in physics.