Thursday, November 20
Milner 317, 4:00 PM
Title: Random matrix theory and the Riemann zeta-function
Abstract: In 1972 a chance meeting between Hugh Montgomery and Freeman Dyson first led people to suspect that there was a relationship between the statistics of the zeros of the Riemann zeta-function and eigenvalues of random matrices. This relationship was developed over the years, notably through data found by Andrew Odlyzko. In 1998 a deeper connection was discovered between the value distribution of the zeta-function and the distribution of values of characteristic polynomials of these random matrices. Today we have an amazing set of parallels between the Riemann zeta-function (also families of L-functions) and unitary matrices (also orthogonal and symplectic matrices). In this talk we will describe some of these connections. We will focus especially on the random matrix side of this duality, and discuss some of the (elementary) techniques that prove the elegant theorems on this side. The talk will be aimed at a general audience.