Exact Results in Quantum Theory

I will give an introductory talk on relations between quantum knot invariants and Chern–Simons theory. The seminal paper by Witten showed that Chern–Simons theory provides a natural framework for the study of 3‐manifolds and knot invariants. I will explain how the path integral formulations of invariants in Chern–Simons theory has led to rigorous formulations in mathematics. In addition, I will mention about the volume conjecture which relates quantum knot invariants to geometry of knot complements in S^3. The talk is supposed to be accessible to both mathematicians and physicists.