Title: Twisted Alexander polynomials of hyperbolic knots

Abstract:  I will discuss a twisted Alexander polynomial naturally
associated to a hyperbolic knot in the 3-sphere via a lift of its
holonomy representation to SL(2, C).  It is an unambiguous symmetric
Laurent polynomial whose coefficients lie in a number field coming
from the hyperbolic geometry.    The polynomial can be defined as the
Reidmeister torsion of a certain acyclic chain complex, namely the
first homology of the knot exterior with coefficients twisted by the
holonomy representation tensored with the abelianization map.   This
polynomial contains much topological information, for instance about
the simplest surface bounded by the knot.   I will present
computations showing that for all 313,209 hyperbolic knots in S^3 with
at most 15 crossings it in fact gives perfect such information, in
contrast with a related polynomial coming from the adjoint
representation of SL(2, C) on it's Lie algebra.  This is joint work
with Stefan Friedl and Nicholas Jackson