University of Illinois at Chicago
Orbit
Structures of ergodic group actions Let G be a countable group acting
ergodically by measure-preserving transformations on a standard probability
space (X,m). The orbits of the action define an equivalence relation R on X
(understood mod null sets). What information about the group G and its action on
X is hidden in the relation R ? In the talk, we shall discuss several recent and
older results about lattices in Lie groups, L^2-Betti numbers, property (T) and
more. This area of research is also related to other fields such as von Neumann
algebras and logic.