# UC San Diego Probability Seminar (2021-2022)

The seminar meets on Thursdays via Zoom from 11 AM to 12 PM PT unless noted otherwise. Please send me an email if you would like to be added to the mailing list or if you have a suggestion for a speaker. Invite links to talks will be sent to the mailing list.

## Winter

January 27: Gaultier Lambert (University of Zurich)

Abstract: This talk aims to report on the fluctuations of traces of powers of a random $$n$$ by $$n$$ matrix $$U$$ distributed according to the Haar measure on the unitary group. This classical random matrix problem has been extensively studied using several different methods such as asymptotics of Toeplitz determinants, representation theory, loop equations etc. It turns out that for any $$k≥1$$, $$\mathrm{Tr} [U^k]$$ converges as $$n$$ tends to infinity to a Gaussian random variable with a super exponential rate of convergence. In this talk, I will explain some of these results and present some recent work with Kurt Johansson (KTH) in which we revisited this problem in a multivariate setting.

February 3: Jiaoyang Huang (Courant Institute and Simons Society of Fellows)

Abstract: TBA

February 17: Nike Sun (MIT)

Abstract: TBA

February 24: Cesar Cuenca (Harvard)

Abstract: TBA

March 3: Tom Hutchcroft (Caltech) - joint with Group Actions Seminar

Abstract: TBA

March 10: Charles Bordenave (CNRS and Institut de Mathématiques de Marseille, France)

Abstract: TBA

* Available dates: January 20, February 10, 24