Marco Barbieri: Strong convergence through the lens of a permutation group enthusiast

A recent breakthrough in random matrix theory is the ability to prove strong convergence using limited combinatorial data, contrasting with the traditionally heavy analytic machinery. This second survey talk focuses on the notion of strong convergence in the setting of permutation groups. In particular, we will examine the proof of strong convergence for the action of the symmetric group of degree n on k-subsets of {1,2,…,n}. The talk is intended to stand independently from the previous one, though it will not revisit the broader motivations behind the topic. Warning! I am far from an expert in the area, thus any comments, questions, or corrections will be very welcome.