Abstract: A well known conjecture in fractal geometry says that the dimension of a self-similar measure on the real line is strictly smaller than its natural upper bound only in the presence of exact overlaps. That is, only if the maps in the generating iterated function system do not generate a free semigroup. I will present recent developments regarding this conjecture, focusing on my joint work with P. Varjú regarding homogeneous systems of three maps.


Zoom meeting details:

Join Zoom Meeting
Meeting ID: 824 6793 6892
Passcode: 2k939h