The degree of the colored Jones polynomial of a knot

Geometry Topology Seminar
Monday, October 11, 2010 - 15:05
1 hour (actually 50 minutes)
Skiles 269
Georgia Tech
Given a knot, a simple Lie algebra L and an irreducible representation V of L one can construct a one-variable polynomial with integer coefficients. When L is the simplest simple Lie algebra (sl_2) this gives a sequence of polynomials, whose sequence of degrees is a quadratic quasi-polynomial. We will discuss a conjecture for the degree of the colored Jones polynomial for an arbitrary simple Lie algebra, and we will give evidence for sl_3. This is joint work with Thao Vuong.