3:00–4:00 pm Eckhart Hall, Room 202
Title: Branching processes in random matrix theory and analytic number theory
Abstract: The limiting distributions for maxima of independent random
variables have been classified during the first half of last century.
This classification does not extend to strong interactions, in
particular to the flurry of processes with natural logarithmic (or
multiscale) correlations. These include branching random walks or the 2d
Gaussian free field. More recently, Fyodorov, Hiary and Keating (2012)
exhibited new examples of log-correlated phenomena in number theory and
random matrix theory. As a result (and as a testing ground of their
observations) they have formulated very precise conjectures about maxima
of the characteristic polynomial of random matrices, and the maximum of
L-functions on typical interval the critical line. I will describe the
recent progress towards these conjectures in both the random and
deterministic setting.