Scientific seminar on the differential and functional differential equation under the guidance of prof. Sternin B. Yu. and prof. Savin A.Yu
Scientific seminar on the differential and functional differential equation under the guidance of prof. Sternin B. Yu. and prof. Savin A.Yu
2019 The event passed
27 Jun
Location
Moscow Russia, 3, Ordzhonikidze st., аud. 471
Contact person
Savin A. Yu.
About the event

Speaker: Maxim Braverman (Northeastern University, USA).

Topic: Тhe spectral Flow of a family of Toeplitz operators.

Abstract:  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 in \mathbb{C}^n. 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 a tight-binding model of topological insulators is a special case of our result. In the appendix, Koen van den Dungen reviewed the main result in the context of (unbounded) KK-theory.

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