Speaker
Emilio Corso, Pennsylvania State University
Abstract
A great deal of interest in fractal geometry centres on determining the dimensional properties of self-similar sets and measures. In joint work with Shmerkin, we establish the expected dimension formula for L^q-dimensions of homogeneous statistically self-similar measures in arbitrary ambient dimension, under the assumptions of exponential separation and unsaturation on lines. Our general framework consists of the class of dynamically driven self-similar measures, which allows for a unified treatment of the deterministic and the random case. The proof relies crucially on an inverse theorem for the L^q-norm of convolutions established recently by Shmerkin.