Adrien Hardy: Universality for complex covariance matrices.

Empirical covariance matrices are ubiquitous random matrix models in applied mathematics. Based on recent collaborations with W. Hachem and J. Najim (CNRS), my talk will describe universal features from random matrix theory arising in these matrix models (Tracy-Widom fluctuations, apparition of the Bessel and the Pearcey kernel), provided the entries are (correlated) complex Gaussian. I'll also discuss cases where universality seems to break down.