Quantum symmetries in operator algebras and mathematical physics

A notion of symmetry has been fundamental in mathematics and physics for many years. A new type of "quantum" symmetry has emerged in theory of operator algebras, quantum groups, quantum invariants in low dimensional topology, integrable systems, vertex operator algebras, quantum field theory and condensed matter physics since 1980's. I will present development in these areas from an operator algebraic viewpoint. Emphasis is given to the Jones theory of subfactors, chiral conformal field theory and two-dimensional topological order. No knowledge on these topics is assumed as a prerequisite.