The A-polynomial, symplectic geometry, and quantisation
by Dan Mathews
Abstract: The A-polynomial is a knot invariant based on the SL(2) representation theory of a knot group. It has long been known to have close connections to hyperbolic geometry, but it has returned with a vengeance in recent years, appearing in various guises from physics, and motivating mathematical statements such as the AJ conjecture. In this talk I'll outline the A-polynomial and some work of Dimofte in which he considered its relation to Chern-Simons theory. In particular, I'll talk about methods to calculate the classical A-polynomial, and its quantisation, via symplectic geometry.