10/19: Florian Richter
Additive and geometric transversality of fractal sets in the reals and integers
Abstract: Using the language of fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the 1960s that explore the relationship between digit expansions of real numbers in distinct prime bases. While his famous x2 x3 conjecture remains open, recent solutions to some of his “transversality conjectures” have shed new light on old problems. In this talk we explore analogues of results surrounding Furstenberg’s conjectures in the discrete setting of the integers, with the aim of understanding the independence of sets of integers that are structured with respect to different prime bases. This is based on joint work with Daniel Glasscock and Joel Moreira.