Abstract:

This talk is motivated by surprising connections between two very different approaches to 3-dimensional topology, and more precisely by the  Kashaev-Murakami-Murakami Volume Conjecture, which relates the growth of colored Jones polynomials of a knot to the hyperbolic volume of its complement. I will discuss a closely related conjecture for diffeomorphisms of surfaces, based on the representation theory of the Kauffman bracket skein algebra of the surface, a quantum topology object closely related to the Jones polynomial of a knot. I will describe partial results obtained in joint work with Helen Wong and Tian Yang.