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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

Donnerstag, 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 Mittwoch, 22.04.2015 15:22 von cgiet_01
Geändert am Montag, 26.02.2018 17:02 von wuebbel
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