16 February 2023, 14:15 (EET), Hall 300, INRNE

• Dr. Yacine Baroumi-Andreani (University of Bochum, visiting INRNE)
• Title: A new approach to the characteristic polynomial of a random unitary matrix
• Abstract: The characteristic polynomial of a random (Haar-distributed) unitary matrix is considered as an interesting toy model for the probabilistic study of the Riemann Zeta function. We will recall the history of the topic starting with the Montgommery-Dyson correspondence, the Keating-Snaith moments conjecture and some recent developments on other functionals. We will then give a conceptual comparison of some of the techniques used in the field and a zoo of results one can achieve, with a particular focus on a recent technique that allows to rederive all the results in a unified way using symmetric function theory and local Central Limit Theorems.
• Slides