Subfactors and Quantum Symmetry

The study of operator algebras was initiated by von Neumann to provide a context for the algebras of observables that arise in quantum mechanics. Since their introduction, operator algebras have come to play a central role in many branches of mathematics and physics. In this talk, we will explain how symmetries of inclusions of operator algebras can be described in the language of tensor categories, providing a link with quantum groups and topological quantum field theory.