Fixed-point properties for random groups

A group is said to have a fixed-point property with respect to some class of metric spaces if any isometric action of the group on any space in the class admits a fixed point.

In this talk, I will focus on fixed-point properties with respect to (classes of) Banach spaces. I will survey some results regarding groups with and without these fixed-point properties and then present a recent result of mine regarding fix-point properties for random groups with respect to l^p spaces.