Projekt

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Analyse géométrique sur les groupes et les variétés

Titel Englisch Geometric Analysis on groups and manifolds
Gesuchsteller/in Valette Alain
Nummer 118014
Förderungsinstrument Projektförderung (Abt. I-III)
Forschungseinrichtung Institut de mathématiques Université de Neuchâtel
Hochschule Universität Neuenburg - NE
Hauptdisziplin Mathematik
Beginn/Ende 01.10.2007 - 30.09.2009
Bewilligter Betrag 589'886.00
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Keywords (12)

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

Lay Summary (Englisch)

Lead
Lay summary
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.
Direktlink auf Lay Summary Letzte Aktualisierung: 21.02.2013

Verantw. Gesuchsteller/in und weitere Gesuchstellende

Mitarbeitende

Verbundene Projekte

Nummer Titel Start Förderungsinstrument
109130 Analyse géométrique sur les groupes et les variétés 01.10.2005 Projektförderung (Abt. I-III)
126689 Analyse géométrique sur les groupes et les variétés 01.10.2009 Projektförderung (Abt. I-III)
130435 Groupes sofiques: algèbre, analyse et dynamique 01.05.2010 Sinergia

Abstract

This is a joint research project, for the whole of Pure Mathematics at the Mathematics Institute at Université Neuchâtel. It consists of two distinct projects:Project A (head: Alain VALETTE): Property (T) and affine actions on Hilbert and Banach spaces.Project B (head: Bruno COLBOIS): Spectral theory on riemannian manifolds and Hilbert geometry.
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