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.