Title: A local view ontopology

Abstract:  In this talk, I revisit topology insolid-state systems from a local perspective. This view highlights qualitativedifferences in the physical response to local perturbations between topologicaland trivial systems, from topological semi-metals to insulators. We will discussthe role of crystalline symmetry and concretize it by analyzing the effect oflocal impurities in these different systems. I will show numerical results forelectron localization in the presence of chemical potential disorder, where wefind rich and unexpected behavior beyond the conventional theory of electronlocalization.