István Kolossváry: Dimension drop and the dual iterated function system for analytic self-conformal sets

The dimension drop conjecture is a long standing open problem in fractal geometry. I will give a brief overview of the question with particular emphasis on a recent result of Rapaport, who confirmed that the exponential separation condition (ESC) implies no dimension drop for analytic self-conformal sets and measures on the real line. In a joint work with Balázs Bárány (BME) and Sascha Troscheit (Uppsala), 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.