Appears in collection : 2024 - T2 - WS3 - Actions of large groups, geometric structures, and the Zimmer program

Super-expanders are sequences of finite, d-regular graphs that satisfy some nonlinear form of spectral gap with respect to all uniformly convex Banach spaces. This notion vastly strengthens the classical notion of expander. In this talk I will explain some recent constructions of super-expanders, coming from actions of higher rank lattices on Banach spaces and on manifolds. I will also review some recent constructions of (usual) expanders, for which we do not know whether they are super-expanders.