### The volume conjecture for small angles. (Stavros Garoufalidis)

### Abstract:

Given a knot in 3-space, one can associate a sequence J(n) of
Laurent polynomials in a variable q, where n=1,2,3... The volume conjecture
states that the evaluation of J(n) at exp(2 pi i a/n) is a sequence of
complex numbers that grows exponentially. Moreover, the growth rate is
proportional to the volume of a corresponding SL(2,C) representation of the
knot complement. In joint work with Thang Le, we will give a proof of the
volume conjecture for small a-angles. Moreover, we will prov the existence
of asymptotic expansions to all orders in n,
for small angles.