Ian Morris

A dimension gap between self-affine measures and self-affine sets.

A classical theorem of J.E. Hutchinson states that every self-similar set satisfying the open set condition admits a self-similar measure with Hausdorff dimension equal to the similarity dimension. I will discuss work in progress with Çağrı Sert in which we show that the analogous statement for self-affine measures on self-affine sets is almost never true: unless an affine iterated function system consists of similarities or is reducible, there is a gap between the maximal Hausdorff dimension of a self-affine measure and the affinity dimension.