Analyse géométrique sur les groupes et les variétés
Project responsable Alain Valette
Team member Simon Roulot
Soyoung Moon
Fabien Crevoisier
Daniele Otera
Van The Lionel Nguyen
Florent Balacheff
Project partner Bruno Colbois
Abstract Project A: Property (T) and affine actions on Hilbert and Banach spaces (head: Alain Valette) The project will deal with two main themes:
-Property (T): relations between various notions of isolation, for non-unitary finite-dimensional representations (in terms of Fell-Jacobson topology, in terms of Banach algebras, cohomologically...); K-theory of the corresponding Banach algebras and link with the existing K-theoretic versions of tensoring with finite-dimensional representations; study of strong forms of property (T) for simple algebraic groups over non-archimedean local fields.
-Affine isometric actions on Hilbert spaces: stability of the class of Haagerup groups (semi-direct products, wreath products, central sequences...); study of affine actions associated with the left regular representation; existence of proper or non-proper (but unbounded) 1-cocycles; study of the structure of orbits in affine actions; geometric group theory and cohomological interpretation of end-depth.

Project B: Spectral theory on Riemannian manifolds and Hilbert geometry (head: Bruno Colbois). This project proposes two directions of research:
- the spectral theory of Riemannian manifolds;
- the study of Hilbert geometries on convex domains in R^n and related topics.
Keywords Kazhdan's property (T), Affine actions, Haagerup property, K-theory of Banach algebras, Ends of groups, Amenable groups, Spectral theory on Riemannian manifolds, Eigenvalues, Differential forms, Extremal metrics, Hilbert geometry, Spaces of nonpositive curvature
Type of project Fundamental research project
Research area Mathématiques
Method of financing FNS Encouragement de projets (Div. I-III)
Status Completed
Start of project 1-10-2007
End of project 30-9-2011
Overall budget 589'886.00
Contact Alain Valette