Large-scale geometry obstructs localization

We explain the coarse geometric origin of fact that certain spectral subspaces topological insulator Hamiltonians are delocalized, in sense they cannot admit an orthonormal basis localized wavefunctions, with respect to any uniformly discrete set localization centers. This is a robust result requiring neither spatial homogeneity nor symmetries and applies Landau levels disordered quantum Hall systems on general Riemannian manifolds.