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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.

Abstract:

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.


Der Vortrag findet im Rahmen eines Zoom-Meetings statt. Bei Interesse an den Zugangsdaten bitte bei Herrn Prof. Mugnolo (delio.mugnolo@fernuni-hagen.de) melden.

mathinf.webteam | 07.01.2022