The ubiquity of logarithmically correlated fields

In 2012 Fyodorov, Hiary, and Keating formulated a striking conjecture: the maxima of log-determinants of large random matrices behave like those of logarithmically correlated fields. Surprisingly, they conjectured that also the Riemann zeta function belongs to this log-correlated group. While there has been huge progress in proving this conjecture, most of the current results are for integrable models. The goal of this project is to establish new analytical techniques to show that this connection holds for a large class of random matrix models, and more. In general, the broad interest of our research group lies at the interface of mathematical physics and probability, with connections to quantum mechanics and potentially to theoretical machine learning