Einladung zum Vortrag (Zoom) von Herrn Prof. Dr. Mostafa Sabri (Universität Kairo) am 02.02.2022 - 14:30 Uhr im Rahmen des Forschungsseminars Analysis[02.02.2022]
Im Rahmen des Forschungsseminars Analysis hält am Mittwoch, den 2. Februar 2022, um 14:30 Uhr,
Herr Prof. Dr. Mostafa Sabri (Universität Kairo)
einen Vortrag zum Thema
Spectral analysis of large quantum graphs.
Quantum graphs are continuum analogs of discrete (combinatorial) graphs in which the adjacency matrix is replaced by a differential operator on the edges. They arise naturally in chemistry, physics and engineering when one considers propagation of waves through a quasi-one-dimensional system, and they are also interesting for purely mathematical reasons.
This talk is intended for a wide audience; I will first introduce quantum graphs then discuss four problems : how to define an appropriate notion of convergence for sequences of quantum graphs ? does this notion guarantee the convergence of empirical spectral measures ? how about the nature of the spectrum at the limit infinite quantum graph ? can we show that in some cases it exhibits absolutely continuous spectrum ? and if yes, what if we consider a sequence of finite quantum graphs converging to such model, are the eigenvectors delocalized in the sense that they are essentially uniformly distributed over the graph ?
This is based on several joint works with Nalini Anantharaman, Maxime Ingremeau and Brian Winn.
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