Jon Keating is Professor of Mathematics and EPSRC senior research fellow. He will review some recent developments in quantum chaos, random matrix theory and the theory of the Riemann zeta function, which plays a central role in number theory. Many of these developments are intimately related to each other and were stimulated by attempts to understand the deep and surprising connections that have emerged in the past few years between the three subjects in question. The works of Professor Keating illuminated these relations.