Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, January 17, 2006.

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Tuesday, January 17, 2006

1:00 pm in 347 Altgeld Hall,Tuesday, January 17, 2006

Transport in the One-Dimensional Schrodinger Equation

Michael Goldberg (JHU Math)

Abstract: The free Schrodinger evolution respects the principle of inertia in the sense that objects at rest tend to remain at rest. In the presence of a generic potential (one without a resonance at zero energy), however, all initial data tends to propagate with nonzero velocity. We will sketch out a proof of this curious phenomenon, and describe what happens instead in the resonant case.

2:00 pm in 243 Altgeld Hall,Tuesday, January 17, 2006

A Jordan domain is CAT(0)

Richard Bishop (UIUC Department of Mathematics)

Abstract: For a Jordan domain in the plane the length metric space of points connected to an interior point by a curve of finite length is a CAT(0) space. With respect to the cone topology, that space plus its boundary at infinity is topologically the same as the original Jordan domain.

4:00 pm in 245 Altgeld Hall,Tuesday, January 17, 2006

Solutions of families of polynomial equations

Jason M. Starr (MIT)

Abstract: Given a system of polynomials depending on parameters, when is there a polynomial map in the parameters whose output is a solution of the system for that choice of parameters? For 1-parameter systems, there is a polynomial map if for a general choice of the parameter every pair of solutions of the system can be connected by a 1-parameter family of solutions, i.e., if the variety is "rationally connected". I will discuss this theorem, the geometric interpretation and some consequences, and a conjecture for 2-parameter systems. Host: S. Katz