Quantum Symmetries

This volume contains the proceedings of the thematic program on ""Quantum symmetries: Tensor categories, topological quantum field theories, and vertex algebras"" held from October 10 -November 4, 2022, at the Centre de Recherches Mathematiques, Montreal, Quebec, Canada. Quantum symmetries is a rapidly expanding area in which tensor categories are applied to mathematical physics, in particular, to conformal and topological quantum field theories. These fields, in turn, connect to a huge variety of modern mathematics, including representation theory, vertex operator algebras, Hopf algebras, link and knot invariants, geometry, subfactors, combinatorics, and so much more. The thematic program on quantum symmetries featured advanced lecture courses and research seminars by international leaders of their respective fields. This proceedings volume is centered on the active research of the area, but also includes an in-depth survey of one of the main topics, $W$-algebras.