Dimension of self-affine measures and additive combinatorics

Informal Group Action Seminar
Topic:Dimension of self-affine measures and additive combinatorics
Speaker:Mike Hochman
Affiliation:HUJI; von Neumann Fellow, School of Mathematics
Date:Wednesday, November 14
Time/Room:2:00pm - 3:15pm/Simonyi Hall 101

The purpose of the talk is to explain how additive combinatorics plays a role in recent work on the dimension of self-affine measures generated by maps satisfying a diophantine condition. Under low-entropy or separation assumptions, this problem is reduced to understanding the linear projections of the measure, and I will mainly discuss this case. The main ingredient is a linearization argument which allows one to transfer results on convolutions on the line to the group-action setting. As time permits I will discuss how to deal with the high-entropy case, which is more complex.