On the disjointness property of groups
Time and place
12:30 PM on Thursday, October 19th, 2017; NAC 6/111
Eli Glasner ( Tel-Aviv University)
Abstract
In his seminal 1967 paper "Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation" Furstenberg introduced the notion of disjointness of dynamical systems, both topological and measure preserving. In this paper he showed, among many other beautiful results, that for the integers the Bernoulli system is disjoint from every minimal system, and then applied this approach to prove his famous Diophantine theorem: If S is a non-lacunary semigroup of integers and a is an irrational, then Sa is dense in the circle R/Z. I will review the development of these ideas during the following decades and introduce a new class of groups, DJ-groups, to which the main disjointness results extend. Amenable and residually finite groups are DJ, and the DJ property extends through short ex- act sequences. In fact, we don’t know if there is any group which is not DJ. This is a joint work in progress with Benjy Weiss.
