Istvan Kolossvary: Verifying the exponential separation condition for analytic self-conformal sets on the real line

Abstract: There is a natural upper bound for the dimension of self-similar sets, usually coined the similarity dimension. On the real line there is a folklore conjecture that the only way that the actual dimension drops below the similarity dimension is if exact overlaps are present. In a breakthrough paper, Hochman confirmed the conjecture assuming the exponential separation condition (ESC). This was recently extended by Rapaport to analytic self-conformal sets on the real line. Together with Balázs Bárány and Sascha Troscheit, we show that the ESC is a topologically typical property, moreover, we give an explicit sufficient condition to verify the ESC by introducing a novel concept that we call the dual iterated function system. I will give an overview of all necessary background before presenting our new results.