Abstract: 

We consider the conformal loop ensembles (CLE) for kappa in (4,8), the regime in which the loops intersect themselves, each other, and the domain boundary.  We describe forthcoming work which aims to associate the gasket of such a CLE (i.e., the set of points not surrounded by a loop) with various canonical metrics as well as consequences for discrete models which converge to such a CLE in the scaling limit, including the existence of the scaling limit of the intrinsic metric and simple random walk on 2D critical percolation clusters.  Based on joint works with Valeria Ambrosio, Irina Dankovic, Maarten Markering, and Yizheng Yuan.

Time：

2:00–3:00 PM, July 21.

Bio-sketch

Jason Miller is a professor at the University of Cambridge and a Fellow of the Royal Society (FRS).