Abstract:

In planar random geometry, a plethora of conformally invariant objects has emerged in the recent decades. Among these, particularly fruitful have been random fractal curves derived from one-dimensional Brownian motion: Schramm-Loewner Evolutions (SLE), Conformal Loop Ensembles (CLE), and their variants. Originally, they were introduced in the context of critical models in statistical physics to understand conformal invariance and critical phenomena upon taking the scaling limit. Indeed, not only do these objects describe critical interfaces in  such models, but they also carry a deep connection to conformal field theory (CFT) - quantum field theory with conformal symmetry,  conjecturally describing the full scaling limit of critical models. In these lectures, I will introduce models for conformally invariant random SLE paths, discuss their relation to critical models, CFT, and its algebraic content.

Time：

9/20 15:30 -17:00 

9/21 10:00 -11:30

9/22 15:30 -17:00

Notes