Vlad Margarint
University of Colorado at Boulder, USA

Schramm-Loewner Evolutions (SLE) were introduced in 2000 by Oded Schramm in order to give meaning to scaling limits of interfaces of some models of Planar Statistical Physics. In the last years, there were many models that were proven to have their interfaces in the scaling limit described by SLE. The SLE curves are studied through the Loewner Differential Equation with a Brownian motion driver. I will present some recent work on extensions of this model in two directions. First, I will present an extension of the dynamics from Brownian Motion driver to Semimartingale driver and secondly from one driver to multiple drivers. A very important example of multiple drivers SLE, due to its connections with Conformal Field Theory (CFT), is the one in which the driver is Dyson Brownian Motion. I will present my recent results in these two directions and discuss also future directions. I will also touch on how another pillar of modern Probability Theory, namely Random Matrix Theory, can bring new insights into the Multiple SLE model.

The last part of my talk will be dedicated to the memory of my friend Octavian Ganea (MIT, Tenure track at NYU) who passed away last year at just 34. Octavian and his family along with a part of the Romanian community and international friends were instrumental in helping me during my degree for the many months in which I had far from enough financial resources to live in Zürich. I will touch on his research achievements in Hyperbolic Neural Networks and beyond, with the scope to popularize his work in Romania, our home country. I will also share some nice memories from our time together at ETH Zürich. Everybody is invited!