Monday 10 March 2025, 16:00 - 17:00 in HG00.062
Koen van den Dungen (Bonn)
Dirac-Schrödinger operators and a Toeplitz index theorem
Dirac-Schrödinger operators are given by Dirac-type operators on a smooth manifold, together with a potential. I will describe a general notion of Dirac-Schrödinger operators with arbitrary signatures (with or without gradings), which allows us to study index pairings and spectral flow simultaneously. There is a general Callias Theorem, which computes the Fredholm index (or the spectral flow) of Dirac-Schrödinger operators in terms of well-known index pairings on a suitable compact hypersurface. I will then focus on the associated Toeplitz operators, which are obtained by compressing the potential to the kernel of the Dirac operator, and I will provide a general index theorem (and a spectral flow theorem) relating Toeplitz operators on the original manifold to Toeplitz operators on the compact hypersurface.