Speaker: Folkmar Bornemann, Technical University of Munich
Date: April 8, 2021
Title: Finite size effects: random matrices, quantum chaos, and Riemann zeros
Abstract: Since the legendary 1972 encounter of H. Montgomery and F. Dyson at tea time in Princeton, a statistical correspondence of the non-trivial zeros of the Riemann Zeta function with eigenvalues of high-dimensional random matrices has emerged. Surrounded by many deep but notoriously intractable conjectures, there is a striking analogy to the energy levels of a quantum billiard system with chaotic dynamics. The statistical accuracy provided by an enormous dataset of more than one billion zeros reveals distinctive finite size effects. Using the physical analogy, we discuss a precise prediction of these effects that has been obtained in terms of operator determinants and their perturbation series (joint work with P. Forrester and A. Mays, Melbourne).