Fernando Rodriguez-Villegas

Arithmetic harmonic analysis on character and quiver varieties

We study connections between the topology of generic character varieties of fundamental groups of punctured Riemann surfaces, Macdonald polynomials, quiver representations, Hilbert schemes on surfaces, modular forms and multiplicities in tensor products of irreducible characters of finite general linear groups.

Mahler's Measure and the Dilogarithm (I)

We continue to investigate the relation between the Mahler measure of certain two variable polynomials, the values of the Bloch--Wigner dilogarithm

Lattice Polygons and the Number 12

D(z)

On the zeros of certain polynomials

and the values

ESTIMATES FOR MAHLER’S MEASURE OF A LINEAR FORM

\zeta_F(2)

Explicit Models of Genus 2 Curves with Split CM

of zeta functions of number fields. Specifically, we define a class

Counting colorings on varieties

\A

Ranks of Elliptic Curves and Random Matrix Theory: Computing central values of L -functions

of polynomials

Mixed Hodge polynomials of character varieties

A

Modular Mahler measures I

with the property that