Department of Mathematical Sciences and MaPhySto
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
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
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
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
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
Do not hesitate to contact the MaPhySto secretariat
or the organizer
for more information.
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January 19, 2004.
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