A new approach to strong convergence (for non-experts)

Abstract. 

In this talk I will provide a friendly introduction to the main ideas behind a new proof technique that allows one to establish sharp norm estimates for random matrix models that, roughly put, possess a lot of symmetry. Among other things, our technique provides a simple proof of Friedman's second eigenvalue theorem, which says that random d-regular graphs are nearly optimal expanders (highly connected networks with very few edges), and permits strengthening Friedman's theorem to show that nearly optimal expanders can be easily constructed using very little randomness.
This is joint work with Chi-Fang Chen, Joel Tropp, and Ramon van Handel.