Caltech Logo

Logic Seminar

Wednesday, January 9, 2019
2:00pm to 3:00pm
Add to Cal
Linde Hall 255
Bernoulli Disjointness
Andy Zucker, Institut de Mathématiques de Jussieu–PRG, Université Paris Diderot,

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)

For more information, please contact Mathematics Department by phone at 626-395-4335 or by email at [email protected].