Logic Seminar

We consider the concept of disjointness for topological dynamical systems, introduced by Furstenberg. We show that for every discrete group, every minimal flow is disjoint from the Bernoulli shift. We apply this to give a negative answer to the "Ellis problem" for all such groups. For countable groups, we show in addition that there exists a continuum-sized family of mutually disjoint free minimal systems. In the course of the proof, we also show that every countable ICC group admits a free minimal proximal flow, answering a question of Frisch, Tamuz, and Vahidi Ferdowsi.

(Joint work with Eli Glasner, Todor Tsankov, and Benjamin Weiss)