Lewis Bowen University of Texas at Austin Does there exist a sequence of free subgroups F_k of the isometry group of hyperbolic n-space such that the Cheeger constant of the quotient space H^n/F_k tends to zero as k tends to infinity? I will explain how to answer this when n is even using L^2 Betti numbers and a generalization of L\"uck approximation due to G. Elek.