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Analyse géométrique sur les groupes et les variétés
Titre du projet
Analyse géométrique sur les groupes et les variétés
Description
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.
-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.
Chercheur principal
Statut
Completed
Date de début
1 Octobre 2007
Date de fin
30 Septembre 2011
Chercheurs
Roulot, Simon
Moon, Soyoung
Crevoisier, Fabien
Otera, Daniele
Nguyen, Van The Lionel
Balacheff, Florent
Organisations
Identifiant interne
16981
identifiant
Mots-clés
1 Résultats
Voici les éléments 1 - 1 sur 1
Publication
Accès libre
The spectral gap of graphs and Steklov eigenvalues on surfaces
2014-2-1, Colbois, Bruno, Girouard, Alexandre