An overview of Quantum Topology
by Professor Stavros Garoufalidis
Abstract: Quantum topology originated in the mid eighties with the discovery of the Jones polynomial of a knot which soon after attracted the attention of Witten, Drinfeld, Kontsevich and others. We will give a short history of this young subject, emphasizing its impact on low dimensional topology and (hyperbolic) geometry, mathematical physics, number theory, representation theory and enumerative combinatorics. We will give a sample of our theorems, and discuss open problems and future directions.