Maxson Lecture Series

Date: April 24, 2018

Time: 4:00PM - 5:00PM

Location: Blocker 117

Speaker: Fernando Rodriguez-Villegas, The Abdus Salam International Centre for Theoretical Physics

Title: Maxson Lecture II: Combinatorics and geometry

Abstract: Thanks to the work of A. Weil we know that counting points of varieties over finite fields yields purely topological information about them. For example, the complex points of an algebraic curve consist of a certain number g, its genus, of donuts glued together. On the other hand the genus determines how the number of points of the curve has over a finite field grows as the size of this field increases.
This interplay between complex geometry, the continuous, and finite field geometry, the discrete, has been a very fruitful two-way street that allows the transfer of results from one context to the other.
I will describe how we may count the number of points over finite fields of certain character varieties and discuss the geometric implications of this computation. The varieties parametrize representations of the fundamental group of a Riemann surface and are related to the moduli space of Higgs bundles on a curve.