Classification and scattering theory for topological insulators

A surprising edge transport, displaying strong robustness to perturbations as an obstruction to Anderson localization, is guaranteed along interfaces separating two-dimensional insulators in different topological phases. We review the classification of several bulk and interface models of topological insulators and analyze their relation via a so-called bulk-edge correspondence. For suitable models, we present a spectral and scattering theory allowing for a quantitative description of the asymmetric edge transport along the waveguide in the presence of perturbations. Time permitting, we will also present recent results on the corresponding inverse scattering theory.