Exceptional projections of self-affine sets: an introduction

Abstract: We describe some recent results on the dimensions of linear projections of self-affine fractals, focusing in particular on an upper bound for the dimension of the projected image. We give a self-contained treatment of this bound and illustrate it through explicit examples, in the process exhibiting some smooth submanifolds of the Grassmannian which can be contained in the exceptional set in Marstrand's theorem.