Informal Group Action Seminar

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.