Colored Jones polynomials and modular formsAlgebra & Discrete Mathematics
|Wed, Feb 28 2018, 4:10PM
In this talk I will discuss joint work with Kazuhiro Hikami, in which we use Bailey pairs and the Rosso-Jones formula to compute the cyclotomic expansion of the colored Jones polynomial of a certain family of torus knots. As an application we find quantum modular forms dual to the generalized Kontsevich-Zagier series. As another application we obtain formulas for the unified WRT invariants of certain 3-manifolds, some of which are mock theta functions. I will also touch on joint work with Robert Osburn, in which we compute a formula for the colored Jones polynomial of double twist knots.