The extremal landscape for the characteristic polynomial of random matrices
The extremal landscape for the characteristic polynomial of random matrices

Ofer Zeitouni, Weizmann
Fine Hall 224
The logarithm of the characteristic polynomial of random matrices shares many characteristics, and some differences, with Gaussian logarithmically correlated fields. This statement, interpreted broadly, is valid for a large class of random matrices. I will review known results and eventually focus on one case, that of $\mathrm{C}\beta\mathrm{E}$ matrices, which leads to a partial resolution of the Keating, Hiary and Fyodorov conjecture.
Based on joint works with Paquette, with Bourgade and Lopato, and with Lambert and Leblé.