MenuMaxson Lecture Series
Spring 2018
| Date: | April 23, 2018 |
| Time: | 3:00pm |
| Location: | Blocker 117 |
| Speaker: | Fernando Rodriguez-Villegas, The Abdus Salam International Centre for Theoretical Physics |
| Title: | Maxson Lecture I: Hypergeometric functions and L-series |
| Abstract: | The classical one-variable hypergeometric functions nFn-1 with rational parameter has a geometric origin. This means that they arise from a one-parameter family of motives. In particular, for each rational value of the parameter we obtain an L-function of rank n. For example 2F1(1/2,1/2;1,t) corresponds in this way to the Legendre family of elliptic curves Et: y2=x(x-1)(x-t). For each rational number t≠0,1 the rank 2 L-function is that of Et. Hypergeometric motives represent a class of motives that is accessible for detail study and still large enough to cover a wide range of features. The talk will focus on the explicit calculation of their L-functions. |
| Date: | April 24, 2018 |
| Time: | 4:00pm |
| 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. |
