Conformal dimension of a set is the minimal Hausdorff dimension of its quasisymmetric image. In the talk, I will discuss the conformal dimensions of various deterministic and stochastic sets, such as Bedford-McMullen sets and self-affine Fractal Percolation Clusters. I will show that the Brownian graph is minimal, i.e. its conformal dimension is equal to 3/2, its Hausdorff dimension.
The talk is based on joint works with Hrant Hakobyan (Kansas State) and Wenbo Li (Toronto).