50 Years of Number Theory and Random Matrix Theory Conference

Abstract:  I will survey recent progress on understanding the value distribution of zeta and L-functions.  In particular I will discuss the problem of moments of the zeta function on the critical line, and central  values of L-functions, where the last twenty five years have seen a conjectural understanding of the asymptotics of these moments, together with progress on obtaining good upper and lower bounds in many situations.