Operator Algebra Seminar

Speaker: Claire Anantharaman-Delaroche (Université d'Orléans) 

Title: Discrete group actions preserving a proper metric. Amenability and property (T)

Abstract : Answering a question of von Neumann, dating back to 1929, it was shown in the 80’s, by van Douwen, that there exist amenable (in von Neumann’s sense) "non trivial" actions of free groups. The class of groups admitting such actions has been studied in the last ten years by several authors. In this talk, I will focus on the case of "non trivial" actions by isometries on locally finite metric spaces. I will mainly study examples of non amenable groups with such amenable actions by isometries and study some properties of these actions. I shall also give a brief overview of the corresponding questions relative to Kazhdan property (T).