Titel: „Recent results on spectral properties of quantum graphs and Archimedean tilings”

Abstract: In the first part of the talk we study the spectrum of finite compact quantum graphs and compare the eigenvalues of two different self-adjoint realizations of a given Schrödinger operator. We derive an explicit expression for the limiting value of the average of the differences of the eigenvalues and discuss its geometrical interpretation. In this context we shall also establish a so-called local Weyl law for general (local) self-adjoint boundary conditions. In the second part of the talk we shall have a look at the discrete normalized Laplacian on Archimedean tilings with the aim of identifying those tilings for which there exist infinitely degenerate eigenvalues (so-called flat bands). Our main purpose will then be to investigate robustness of existing flat bands with respect to perturbations of the Laplacian. Our investigations will lead to the identification of one particular Archimedean tiling - the Super–Kagome tiling – whose spectral properties are outstandingly rich. This talk is based on joint work with P. Bifulco (Hagen), M. Täufer (Hagen), and J. Wintermayr (Wuppertal).

Der Vortrag findet statt am Mittwoch, den 12.07.2023 um 17:15 Uhr im Raum W01 0-006

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