On the geometry of character varieties

Tuesday, January 4, 2011 - 2:00pm - 3:00pm
Keller 3-180
Fernando Rodriguez Villegas (The University of Texas at Austin)
We know, thanks to the Weil conjectures, that counting points of
varieties over finite fields yields purely topological information
about them. In this talk I will first describe how we may count the
number of points over finite fields on the character varieties
parameterizing certain representations of the fundamental group of a
Riemann surface into GL_n. The calculation involves an array of
techniques from combinatorics to the representation theory of finite
groups of Lie type. I will then discuss the geometric implications of
this computation and the conjectures it has led to.

This is joint work with T. Hausel and E. Letellier