Joint SISSA-ICTP Colloquium - Large Random Matrices and beyond - Alice Guionnet

Large random matrices were born about a century ago in the work of the statitician Wishart to analyse big array of noisy datas. It was then shown in the fifties by Wigner and Dyson to be a good model for the Hamiltonian of certain heavy nuclei, hence finding its way in quantum physics. Even more surprisingly, Montgomery gave a numerical evidence that random matrices are intimately related with the zeroes of Riemann Zeta function in the seventies. During the last thirty years, random matrix theory developed as a mature field. In this talk, after underlying a few other domains where random matrices play a central role, I will discuss the random matrix theory of Bernoulli Matrices, presenting old and new results as well as open problems.

Alice Guionnet is a French mathematician known for her work in probability theory, in particular on large random matrices. She has been a pioneer in large deviation principles and heavy tail distribution of random matrices. She has held positions at the Courant Institute, Berkeley, MIT, and ENS (Paris). She is currently a Director of Research at ENS de Lyon. For her work she has received many international recognitions among which the Rollo Davidson Prize, the Loève Prize, the Blaise Pascal Medal of the European Academy of Sciences. In 2017 she was elected to the French Academy of Sciences and Academia Europaea.In 2022 she was elected as an international member to the National Academy of Sciences (USA) and International Honorary Member of the American Academy of Arts and Sciences (AAAS). She has been invited speaker at the European Congress of Mathematics (ECM) 2004, International Congress of Mathematics (ICM) 2006. She has been plenary speaker at the International Congress of Mathematical Physics 2009, IEEE ISIT 2019, ECM 2020 and ICM 2022.