Skip to content

NAG

Seminar

On the mixed Hodge polynomials of character varieties of Riemann surfaces

Rodriguez-Villegas, F (Texas at Austin)
Thursday 17 December 2009, 11:30-12:30

Seminar Room 1, Newton Institute

Abstract

I will describe a calculation of the number of points over finite fields of the varieties of the title (parameterizing generic representations of the fundamental group of a Riemann surface into GL_n). Since the varieties are polynomial count this calculation yields their E-polynomial (a geometric invariant). The results are best expressed in terms of a generating function involving the Macdonald polynomials of combinatorics. We conjecture that a natural deformation of these formulas in fact gives the full mixed Hodge polynomial of the varieties. This is joint work with T. Hausel and E. Letellier.

Video

The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.

Back to top ∧