Agenda de l’IDP

Séminaire Orléans

An introduction to Property (T) and friends
Talia Fernos
Tuesday 14 October 2008 14:00 -  Orléans -  Salle de Séminaire

Résumé :
Property (T) has had many successes in the study of a broad range of areas: von Neumann Algebras, dynamics, and geometric group theory to name a few. It is a property of groups that was introduced by Kazhdan in 1967; he showed that all higher rank lattices share this property. All property (T) groups are finitely generated. This is a key ingredient in Margulis' Arithmeticity Theorem for higher ranks lattices. Simply stated, property (T) is a type of deformation rigidity for unitary representations. Namely, unitary representation which are close to containing the trivial representation actually do. Property (T) can be seen as an analytical (versus geometric) property: it is an invariant under measure equivalence but not under quasi isometry. Property (T) groups do not admit non-trivial actions on many ``simple'' spaces. Such spaces include trees, the circle (with a sufficiently smooth action), and wall spaces. In this talk we will give a survey of property (T) and related properties such as relative property (T), amenability, and a-(T)-menability. We also discuss some recent developments and open questions.

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