Maxson Lecture Series
The Maxson Lecture Series honours Professor Emeritus
Carl Maxson, who
was a member of the Texas A&M Mathematics Department from 1969 until
his retirement in 2002. This annual event is made possible by a
generous endowment from Dr. Maxson's first doctoral student, Professor
Ponnammal Natarajan of Chennai, India.
The Maxson Lectures for the year 2018 will be delivered on April 23 and 24
by:
Fernando
RodriguezVillegas
Head of the Mathematics Section
The Abdus Salam International Centre for Theoretical Physics

Date Time 
Location  Speaker 
Title – click for abstract 

04/23 3:00pm 
Blocker 117 
Fernando RodriguezVillegas The Abdus Salam International Centre for Theoretical Physics 
Maxson Lecture I: Hypergeometric functions and Lseries
The classical onevariable hypergeometric functions _{n}F_{n1} with rational parameter has a geometric origin. This means that they arise from a oneparameter family of motives. In particular, for each rational value of the parameter we obtain an Lfunction of rank n. For example _{2}F_{1}(1/2,1/2;1,t) corresponds in this way to the Legendre family of elliptic curves E_{t}: y^{2}=x(x1)(xt). For each rational number t≠0,1 the rank 2 Lfunction is that of E_{t}. 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 Lfunctions. 

04/24 4:00pm 
Blocker 117 
Fernando RodriguezVillegas The Abdus Salam International Centre for Theoretical Physics 
Maxson Lecture II: Combinatorics and geometry
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 twoway 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.
