Colloquium Mathematics - Dr. Max Lein

Title:

Maxwell-type Operators — A New Class of Operators Describing Classical Waves

Abstract:

Over the last few decades lot research has been dedicated to the study of Schrödinger operators such as $H = -\Delta + V$, and researchers nowadays have access to a rich toolbox of mathematical techniques. Recently, physicists have managed to realize analogs of quantum phenomena with classical waves such as topological insulators. The mathematical basis for these \emph{quantum-wave analogies} is that many classical wave equations can be recast in the form of a Schrödinger equation. Here,\emph{Maxwell-type operators} $M = W \, D$ take the place of a Schrödinger operator $H$. However, since these operators are the \emph{product} of weights $W$ and a free operator $D$, techniques initially developed for Schrödinger operators do not extend without significant work. In this talk I will give an overview over some recent rigorous results and detail some of the complications that arise when adapting e. g. pseudodifferential and semiclassical techniques.

Colloquium coordinators are Prof.dr. A.J. van der Schaft (a.j.van.der.schaft rug.nl),

Dr. A.V. Kiselev (e-mail: a.v.kiselev rug.nl)