# Colloquium abstracts

**Indira Chatterji***

Université de Nice

March 24, 2022

**Property (T) versus aTmenability**: A group has property (T) if its trivial representation is isolated in the unitary dual. This is equivalent to saying that any action by affine isometries on a Hilbert space has a fixed point. A group is called aTmenable if it admits a proper action on a Hilbert space. We shall review those properties and see what happens when we replace the Hilbert space by an ell^p space.