Friday, April 12, 2002
Jack Brown (Auburn)
Experiences of one high-tech migrant worker
2:30 pm / CH 405

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.

Friday, March 15, 2002
José F. Escobar (Cornell)
Harmonic Functions and Geometry
2:30 pm / CH 405

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).

Friday, February 8, 2002
Henghui Zou (UAB)
A Cauchy-Liouville theorem for quasilinear elliptic equations
2:30 pm / CH 405

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.

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.

Friday, December 7, 2001
Thomas Daly (UAB, Pathology)
A mathematical model of gene transfer
2:30 pm / CH 445

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.

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.