Topological Levinson’s theorem for half-line Schrödinger operators

par Dr Hideki Inoue

vendredi 11 juin 2021, 14:00 → 15:00 Europe/Paris

Salle Fokko (Institut Camille Jordan)

Levinson’s theorem is a fundamental result in quantum scattering theory, which relates the number of bound states and the scattering part of the underlying quantum system. For the last about ten years, it has been proved for several models that once recast in an operator algebraic framework this relation can be understood as an index theorem for the wave operators. In this talk, we first review the background and the framework of our investigation. Then we provide analytical and topological results for Schrödinger operators on the half-line. As time permits, we also discuss an ongoing application to a model arising from group theory.