Department of Mathematical Sciences and MaPhySto
Aalborg University
Workshop on
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.