Past lectures

Abstract

This course will be a self-contained introduction to Conformal Loop Ensembles. These are natural random collections of loops in a domain; their study is very closely related to a number of (if not all) questions involving randomness and conformal invariance.

Along the way, we will define and study some properties of:

- Planar Brownian paths, excursions and loops,

- Schramm-Loewner Evolutions (SLE),

- The Gaussian Free Field,

and relations between all these items.