Title: Stochastic fractals: conformal dimension.

Abstract: The conformal dimension of a set is defined as the infimum of the Hausdorff dimensions of all its quasisymmetric images. In this talk, I will explore the conformal dimensions of a variety of both deterministic and stochastic fractal sets. These include classical examples such as Bedford–McMullen carpets, as well as more complex random constructions like self-affine fractal percolation clusters. A highlight of the talk will be a proof that the graph of Brownian motion is minimal—its conformal dimension equals its Hausdorff dimension of . The talk is based on joint work with Hrant Hakobyan (Kansas State University) and Wenbo Li (Tsinghua University).