Marco Barbieri: Strong convergence and random graphs

A recent breakthrough in random matrix theory is the ability to prove strong convergence using limited combinatorial data, in contrast with the heavy analytic techniques previously required. This survey talk will introduce the notion of strong convergence and review some of its recent applications to random models of graphs, hyperbolic surfaces and surface groups. Time permitting, we will outline the proof of the new method for establishing strong convergence. Warning! I am far from an expert in the area, thus any comments, questions, or corrections will be very welcome.