Tutorial Lecture: Gregory Lawler (University of Chicago)

Wednesday 1:30-3:00 and 3:30-5:00

Title: GFF, GMC, SLE, LQG and other Conformally Invariant TLAs

Abstract: I will introduce some key concepts used in conformally invariant systems. The starting point will be the Gaussian Free Field and its relationship to Markov chains and processes. There will be an emphasis on the idea of “exploration’’. I will start with discrete and then go the continuous.

Exploration leads to considering particular curves, Schramm-Loewner evolutions (SLE) and (local) martingales for SLE can be written as exponentials of a GFF. These lead to random metrics and measures on domains. I will relate them to another measure, Minkowski content.