After a brief introduction on the random matrix applications to number theory, I will present a collection of moment computations over the unitary, symplectic and special orthogonal random matrix ensembles that I've done throughout my thesis. I will highlight work on the asymptotics of moments of the logarithmic derivative of characteristic polynomials evaluated near the point 1. Throughout, the focus will be on the methods used, the motivation from number theory and directions for future work.

Online stream:


https://teams.microsoft.com/l/meetup-join/19%3ameeting_N2E1YzU4MjYtNjliZS00YWUyLTk1OTItZDQ4NjBmZjNiYzcw%40thread.v2/0?context=%7b%22Tid%22%3a%228370cf14-16f3-4c16-b83c-724071654356%22%2c%22Oid%22%3a%224a0ba08d-9616-4f3a-9e48-b4ecd5cbbf35%22%7d