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Address: Mathematics
| University of Alabama at Birmingham
1300 University Blvd | Birmingham, AL 35294-1170
Phone: 943 2154 | Fax: 934 9025
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- Friday, April 12, 2002
Jack Brown (Auburn)
Experiences of one high-tech migrant worker
2:30 pm / CH 405
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- Friday, April 5, 2002
Ling Hsiao (Academia Sinica)
Mathematical problems and analysis in semiconductors
2:30 pm / CH 405
Abstract.
We will discuss a number of mathematical modeles used in
semiconductors and the related mathematical analysis. The emphasis is on
various fluid dynamic models, such as drift-diffusion model,
hydrodynamic model, etc., and the relations among these models.
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- Friday, February 22, 2002
Jan Aarts (TU Delft)
The Silver Number
2:30 pm / CH 405
Abstract.
The silver number is defined as the real root of the equation 1 + X = X3.
It was christened by Midhat J. Gazale in his book "Gnomon, from
the pharaohs to fractals", Princeton University Press 1999. The June
1996 issue of Scientific American has an article by Ian Stewart about
the silver number. The silver number shares many properties with the
golden ratio, the positive root of the equation 1 + X = X2. Both
numbers play an important role in arts and architecture. The French
architect, Le Corbusier, has designed a system of measures that is
based on the golden ratio. The American architect, Padovan, made a
system that is based on the silver number. In this talk we shall
discuss several properties that are shared by the golden and silver
numbers. The common properties are both algebraic and geometric in
nature. We shall address which properties make the numbers unique
(excluding the existence of bronze numbers).
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- Friday, February 8, 2002
Henghui Zou (UAB)
A Cauchy-Liouville theorem for quasilinear elliptic equations
2:30 pm / CH 405
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Friday, January 25, 2002
Robert Seiringer (Princeton)
Rigorous Results on the Interacting Bose Gas
2:30 pm / CH 405
Abstract.
We present a summary of recent results on the interacting Bose
gas, that were obtained partly in joint work with Elliott Lieb and Jakob
Yngvason. The ground state of a dilute Bose gas in a trap, as considered
in recent experiments, is usually described by means of the
Gross-Pitaevskii equation, a non-linear one-particle Schroedinger
equation. We clarify its status as an approximation to the quantum
mechanical many-body ground state problem. In addition, we prove the
existence of Bose-Einstein condensation in the dilute limit. Finally, we
discuss the generalization of our results to rotating systems, and
investigate the effect of a breaking of the rotational symmetry.
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Friday, January 18, 2002
Marcel Griesemer (UAB)
Shiny Atoms
2:30 pm / CH 405
Abstract.
The purpose of this talk is to give an introduction to the
(quantum-) theory of light interacting with matter. I will begin
with a short history of quantum physics, discuss angular momentum
and the representation theory of SO(3), and comment on the
connection between symmetries and conservation laws in classical
and quantum mechanics. Finally some of the mathematical
properties of quantum electrodynamics will be described using a
toy model for a Hydrogen atom interacting with light.
About half of the talk will be comprehensible for everybody who
knows calculus and can solve a separable ODE. At the end, you will
have the opportunity to do a small experiment and get some hands
on experience with quantum physics.
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Friday, December 7, 2001
Thomas Daly (UAB, Pathology)
A mathematical model of gene transfer
2:30 pm / CH 445
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Friday, November 30, 2001
John Johnstone (UAB, Computer Science)
Geometric modeling, through the eyes of a mathematician
2:30 pm / CH 445
Abstract.
Geometric modeling is an area of research in computer graphics and
computer science that is closely tied to many areas of mathematics,
such as algebraic geometry and differential geometry. We will discuss
our research on various problems in geometric modeling, their
applications in graphics, robotics, manufacturing, and biomedical
visualization, their relationship to mathematics, and some remaining
open problems. Examples include bitangency and algebraic geometry,
quaternion splines and Riemannian geometry, and contour reconstruction
and topology.
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Friday, November 16, 2001
Nandor Simanyi (UAB)
Transitive Group Actions --- Geometry and Ergodicity
2:30 pm / CH 445
Abstract.
I will give a brief overview of the relationship between the
transitivity of certain group actions on the sphere of velocities and
the ergodic properties (chaotic properties) of billiards with cylindric
scatterers. I will mostly focus on a ``toy example'', one of the
simplest cylindric billiards: We take the four-dimensional flat torus
$\Bbb T^4=\Bbb R^4/\Bbb Z^4$, remove the tubular neighborhoods $C_1$
and $C_2$ of two 2-D translated subtori (the cylindric scatterers),
consider the remaining connected set $\Bbb T^4\setminus(C_1\cup C_2)$
as the billiard table, and investigate the chaotic properties of the
arising dynamical system. Take the group $G$ algebraically generated by
all rotations about the generator spaces of the cylinders $C_i$. It
turns out that the considered dynamical system is ergodic (chaotic) if
and only if the natural action of $G$ on the unit sphere of $R^4$ is
transitive. On the other hand, this transitivity can be easily verified
by taking a close look at the relative position of the two generator
subspaces of the cylinders.
In connection with the above, I will formulate a far-reaching
conjecture.
My talk is to target a general, mathematically mature audience,
including graduate students.
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