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Folkmar Bornemann: Finite size effects: random matrices, quantum chaos, and Riemann zeros

Submitted by Jorge Cisneros on April 8, 2021 - 12:00pm
Folkmar Bornemann

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).

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