Random Matrix Theory and Number Theory
Over the last 35 years, evidence has accumulated hinting
at profound connections between random unitary matrices and the
theory of the Riemann zeta function. (The zeta function encodes
information about the primes and is the subject of the Riemann
Hypothesis, one of the central problems in Pure Mathematics.) In
recent years, a general understanding has developed which sets this
in much wider story, linking a range of fundamental problems in
number theory to properties of random matrices. This talk will be a
survey of the some of the key ideas and developments.