Carolin Gietz

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

Mathematik und Informatik

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.

Angelegt am 22.04.2015 von Carolin Gietz
Geändert am 26.02.2018 von Frank Wübbeling
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Kolloquium Wilhelm Killing
Highlights des FB10
John von Neumann-Lecture