István Kolossváry: On the existence of the box dimension of a set

The box counting dimension of a set is defined through a limit which may or may not exist. There is a folklore conjecture that this limit exists for all self-affine sets. Counterexamples are known if one weakens strict self-affinity. I will survey some of these interesting constructions and then turn to a recent joint work with Balázs Bárány and Antti Käenmäki in which we give further strong support for the conjecture. It is derived as the corollary of the main result of the paper: an all-directions Marstrand-Mattila type projection theorem onto lines for self-affine measures and sets in R^d.