Knots, 3-manifolds, and SL(2,C) character varieties

In this talk, I will begin with a brief review of character varieties in the
SL(2,C) setting a la Culler and Shalen, including an outline of the main
applications to knots and 3-manifolds. I will then give a report on recent joint
work with C. Curtis on the SL(2,C) Casson invariant for 2-bridge knots, and on a
non-triviality result for the M-degree of the A-polynomial of any non-trivial knot.