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Topological Levinson’s theorem for half-line Schrödinger operators
Salle Fokko (Institut Camille Jordan)
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.