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Irreducible group actions by affine isometries on Hilbert spaces

Amenability, coarse embeddability and fixed point properties December 06, 2016 - December 09, 2016

December 06, 2016 (11:00 AM PST - 12:00 PM PST)
Speaker(s): Bachir Bekka (Université de Rennes 1)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Unitary representations

  • affine actions on Hilbert spaces

  • Amenability

  • a-T-menability

  • expander graph

  • index theory

  • non-commutative geometry

  • fixed point properties

  • hyperbolic groups

  • Banach space

  • functional analysis

  • group cohomology

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Abstract

Important classes of locally compact groups are characterized by their actions by affine isometries on Hilbert spaces (groups with Kazhdan's property, a-T-menable groups aka groups with the Haagerup property). We will be interested on the question of irreducibility of such actions, in the sense that the only non empty closed invariant affine subspace is the whole space. This notion was extensively studied in a recent joint work of T. Pillon, A. Valette and myself. We will report on this work as well as on some further results. Special attention will be paid to affine actions whose linear part is a factorial representation, that is, a representation which generates a factor in the von Neumann algebra sense

Supplements
27467?type=thumb bekka Notes 147 KB application/pdf Download
Video/Audio Files

14639

H.264 Video 14639.mp4 338 MB video/mp4 rtsp://videos.msri.org/data/000/027/226/original/14639.mp4 Download
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