Phase Transition in Some Random Matrix Models

After a quick introduction to some of the ideas of random matrix theory, I shall focus on current efforts to prove the existence of phase transition  in some random matrix models suggested by noncommutative geometry. No prior knowledge of RMT or NCG will be assumed in my talk. The talk is based on my recent papers arXiv:2006.02891: Phase transitions in random noncommutative geometries, arXiv:1906.09362: Random finite noncommutative geometries and topological recursion.