Wilhelm Killing Kolloquium: Prof. Dr. Antti Knowles (University of Geneva): Random graphs as models of quantum disorder
Thursday, 11.04.2024 14:15 im Raum M4
A disordered quantum system is mathematically described by a large Hermitian random matrix. One of the most remarkable phenomena expected to occur in such systems is a localization-delocalization transition for the eigenvectors. Originally proposed in the 1950s to model conduction in semiconductors with random impurities, this phenomenon is now recognized as a general feature of wave transport in disordered media, and is one of the most influential ideas in modern condensed matter physics. A simple and natural model of a disordered quantum system is given by the adjacency matrix of a random graph. I report on recent progress in analysing the phase diagram for the Erdös-Renyi model of random graphs. In particular, I explain the emergence of fully localized and fully delocalized phases, which are separated by a mobility edge. Joint work with Johannes Alt and Raphael Ducatez.
Angelegt am Wednesday, 07.02.2024 10:57 von Claudia Lückert
Geändert am Tuesday, 05.03.2024 15:28 von Claudia Lückert
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Wilhelm Killing Kolloquium: Prof. Dr. Tobias Weth (Universität Frankfurt): The geometric impact of overdetermined boundary value problems
Thursday, 25.04.2024 14:15 im Raum M4
In the context of fairly simple elliptic partial differential equations, overdetermined boundary conditions arise in the search of optimal shapes in a broad range of problems, e.g., in fluid mechanics, the theory of elasticity, electrostatics and integral geometry. Due to their relevance, the resulting overdetermined boundary value problems are addressed in prominent conjectures. The Berestycki-Caffarelli-Nirenberg conjecture from 1997, disproved by Sicbaldi in 2010, has lead to various recent results on the existence and classification of extremal unbounded domains. These unbounded optimal shapes can be regarded as analogues of constant mean curvature surfaces governed by nonlocal effects. Schiffer?s conjecture, and the related Pompeiu problem in integral geometry from 1929, are still open.
In my talk, I will discuss a choice of classical and recent results on overdetermined boundary value problems, including joint work with M.M. Fall and I.A. Minlend.
Angelegt am Wednesday, 21.02.2024 14:09 von Claudia Lückert
Geändert am Friday, 23.02.2024 11:13 von Claudia Lückert
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