Non-interacting orbital magnetism and bulk-edge correspondence for both Schrödinger and Dirac operators

The main purpose of the talk is to explain what bulk-edge correspondence is for people who, like myself, think that plain operator theory and functional analysis could do as well as K and KK theory. I will present previous and ongoing work with J.-M. Barbaroux, L. Le Treust (Marseille \& Toulon), M. Moscolari (Milano), S. Teufel (Tübingen), E. Stockmeyer (Santiago de Chile), K.S. Sørensen (Aalborg), and N. Raymond (Angers). They cover the Schrödinger case doi.org/10.1007/s00023-024-01501-7, the pure Dirac-Landau case link.springer.com/article/10.1007/s11005-024-01839-3 and the general "infinite mass" Dirac case arxiv.org/abs/2509.17151.