Research Project:

We will study expanders with respect to general metric spaces and more specifically Hadamard spaces. The starting point is the construction by Lafforgue of super-expanders: classical expanders which are also expanders with respect to every uniformly convex normed space. Recently, Mendel-Naor gave a different construction of super-expanders, using zig-zag product. They also provided explicit example of a sequence of 3-regular graphs which are expanders with respect to a Hadamard space X but random regular graphs are not expanders with respect to X. Our main goal is to build new natural examples of this kind with respect to explicit expander sequences coming from linear groups.