The spectral Flow of a family of Toeplitz operators

27.04.2018, 10:30 Uhr  –  Haus 9, Raum 2.22
Arbeitsgruppenseminar Analysis

Maxim Braverman (Northeastern University)

We show that the (graded) spectral flow of a family of Toeplitz operators on a complete Riemannian manifold is equal to the index of a certain Callias-type operator. When the dimension of the manifold is even this leads to a cohomological formula for the spectral flow.

As an application, we compute the spectral flow of a family of Toeplitz operators on a strongly pseudoconvex domain. This result is similar to the Boutet de Monvel's computation of the index of a single Toeplitz operator on a strongly pseudoconvex domain.

Finally, we show that the bulk-boundary correspondence in the Graf-Porta model of topological insulators is a special case of our result.