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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

Department of Mathematical Sciences and MaPhySto
Aalborg University

Workshop on

Mathematical Physics

Thursday September 2, 1999


10:00 - 11:00
Helge Holden (Norwegian University of Science and Technology, Trondheim, Norway): Hierarchies of soliton equations and their algebro-geometric solutions
Abstract. Nonlinear partial differential equations admitting soliton equations, the most well-known being the Korteweeg-de Vries equation (KdV), have been studied extensively. Special attention has been given to algebro-geometric solutions (where solitons are just a special case); and techniques from various areas of mathematics are needed to understand their behavior. One possible method is to introduce hierarchies of equations, and study algebro-geometric solutions of these equations. We will apply this technique to the KdV hierarchy, the AKNS hierarchy, and the sine-Gordon hierarchy. My talk is based on joint work with F. Gesztesy, Missouri.

11:10 - 12:10
Vojkan Jaksic (University of Ottawa, Canada): Spectral theory of corrugated surfaces
Abstract. I will discuss spectral and scattering properties of the discrete Laplacian limited to a half-space. The interesting properties of such operators stem from the imposed boundary condition described by a function (surface potential) $V$. I will consider the cases where $V$ is a deterministic, random and quasi-periodic potential. This talk is based on joint work with Y. Last and S. Molchanov.

12:10 - 13:00
Lunch. To participate in the lunch, please register.

13:00 - 14:00
Erik Skibsted (University of Aarhus). Quantum scattering for homogeneous of degree zero potentials: Absence of channels at local maxima and saddle points
Abstract. A report on recent joint work with I. Herbst, University of Virginia.

14:00 - 14:30
Coffee and Tea

14:30 - 15:30
Pavel Exner (Academy of Sciences, Prague, Czech Republic): Anomalous bound states of a Pauli electron
Abstract. We consider a two-dimensional Pauli electron with an anomalous magnetic moment, $g>2$, interacting with a non-homogeneous magnetic field $B$ perpendicular to the plane. If $supp\ B$ is compact and the corresponding flux is $F\geq 0$, we show that there are at least $1+[F]$ bound states, a sligtly weaker result is obtained for field with tails. We also analyze the strong- and weak-field behaviour of the discrete spectrum.

More Information

Do not hesitate to contact the MaPhySto secretariat (at maphysto@maphysto.dk) or the organizer Arne Jensen for more information.

This document, http://www.maphysto.dk/oldpages/events/W-on-MP1999/index.html, was last modified January 19, 2004. Questions or comments to the contents of this document should be directed to maphysto@maphysto.dk.