8. John von Neumann Lecture: Prof. Dr. Eli Glasner (Tel Aviv University):
Kazhdan's Property T and the Geometry of the Collection of Invariant Measures
Thursday, 25.06.2015 16:30 im Raum M5
Abstract. In the mid-1960s D. Kazhdan introduced the definition of property T
for locally compact groups in terms of their unitary representations. I will describe
another approach to this notion which relies on Ergodic Theory and the notion of
strong ergodicity. For a countable group G and an action (X;G) of G on a compact
metrizable space X, let MG(X) denote the simplex of probability measures on X
invariant under G. The natural action of G on the space of functions = f0; 1gG,
will be denoted by (;G). I will present two main results.
(i) If G has property T then for every G-action the simplex MG(X), when non-
empty, is a Bauer simplex (i.e. the set of ergodic measures (extreme points) in
MG(X) is closed).(ii) G does not have property T if the simplex MG() is the Poulsen simplex (i.e. the ergodic measures are dense in MG()).Some applications and more recent developmnts will also be indicated.