Vlad Margarint: Law of the Schramm-Loewner Evolution (SLE) tip, and a bridge between Multiple SLEs and Random Matrix Theory

Abstract:

In the first part of the talk, I will introduce some basic ideas of SLE theory, and discuss one of our results in the one SLE curve case, concerning the law of the SLE tip at a fixed time. In the second part of the talk, I will focus on the multiple SLE curves, and I will describe a new toolbox that connects Multiple Schramm-Loewner Evolutions (SLE) and Random Matrix Theory. One aspect of this research direction is centered in an interacting particle systems model, namely the Dyson Brownian motion. I will describe the connection with Random Matrix Theory via a first application of our method. I will also discuss some open problems that emerge both in the one SLE curve and Multiple SLE curves picture. The first part is a joint work with O. Butkovsky and Y. Yuan, and the second part is a joint work with A. Campbell and K. Luh.