Workshop on Mathematical Physics, September 1999

Mathematical Physics

Thursday September 2, 1999

Schedule

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.