Branching Processes in Random Matrix Theory and Analytic Number Theory

Explore the fascinating intersection of branching processes, random matrix theory, and analytic number theory in this hour-long lecture by Maksym Radziwill. Delve into the classification of limiting distributions for maxima of independent random variables and its limitations when dealing with strong interactions. Examine log-correlated phenomena in number theory and random matrix theory, focusing on the groundbreaking work of Fyodorov, Hiary, and Keating. Investigate precise conjectures about maxima of characteristic polynomials of random matrices and L-functions on the critical line. Gain insights into recent progress towards these conjectures in both random and deterministic settings, and discover how branching random walks and the 2D Gaussian free field relate to these cutting-edge mathematical concepts.