Abstract: A conjecture of Singer predicts that the L^2-Betti numbers of the universal cover of a closed aspherical manifold vanishes outside of the middle dimension. In this talk, we will prove the conjecture for some manifolds constructed using right-angled Coxeter groups. I will also talk about connections to homology growth of right-angled Coxeter groups (with various coefficients).
All joint work with Grigori Avramidi and Boris Okun.