Singularity versus exact overlaps for self-similar measures

I will present a recent preprint by Károly Simon and Lajos Vágó entitled "Singularity versus exact overlaps for self-similar measures". The main goal of the paper is to give a negative answer to the following question: is it true for a self-similiar measure on the real line having similarity dimension greater than one, that it is singular only if there is exact overlap. Counterexamples are found in the family of projections of the standard self-similar measure on the Sierpiński carpet. The proof is not constructive.