Moments of the Riemann Zeta Function

An important area of study in analytic number theory is the average behaviour of the Riemann zeta function on the critical line

Re(s) = 1/2. I'll talk a bit about what we know so far, and how random matrix theory helps us predict even more. If time permits, I'll discuss how one can generalise this to the average behaviour of families of L-functions at the critical point s = 1/2.