Our colloquium takes place on the first Tuesday of each month from 15:30 to 16:30, usually in room A709.
A renowned expert (being an excellent speaker as well) visits us for an afternoon and gives a panorama of one of her research areas. The talk is meant to be accessible to all members of the lab, including PhD students in analysis, game theory, probability and statistics. Ideally, it should start gently with an historical background on the problem and an overview of the main questions and applications, keeping a non technical style during at least the first half of the talk. Of course it is also nice to have a part with more mathematical details: the most appreciated colloquia were those in which the speaker succeeded to develop a nice technical idea or an elegant argument that everyone should know.
Food and drinks are served after the event, usually in Espace 7!
Date: Tuesday, June 2nd 2026 (15:30-16:30, room A709)
Speaker: (Université de Genève)
Title: Random graphs as models of quantum disorder
Abstract: A disordered quantum system is mathematically described by a large Hermitian random matrix. One of the most remarkable phenomena expected to occur in such systems is a localization-delocalization transition for the eigenvectors. Originally proposed in the 1950s to model conduction in semiconductors with random impurities, the phenomenon is now recognized as a general feature of wave transport in disordered media, and is one of the most influential ideas in modern condensed matter physics. A simple and natural model of such a system is given by the adjacency matrix of a random graph. I report on recent progress in analysing the phase diagram for the Erdös-Renyi model of random graphs. In particular, I explain the emergence of fully localized and fully delocalized phases, which are separated by a mobility edge. I also explain how to obtain optimal delocalization bounds using a new Bernoulli flow method. Based on joint work with Johannes Alt, Raphael Ducatez, and Joscha Henheik.