SEMINARS
Updated: 5-17-2006
   
MAY 22- 26, 2006
   
Special Analysis Seminar
Topic: Derivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensates
Presenter: Benjamin Schlein, Harvard University
Date:  Tuesday, May 23, 2006, Time: 3:00 p.m., Location: Fine Hall 314
Abstract:

In this talk I am going to report on a recent result obtained in collaboration with L. Erdoes and H.-T. Yau. We consider a system of N interacting bosons in the Gross-Pitaevskii limit, where N tends to infinity and the scattering length of the pair potential is of the order 1/N.  In this limit we prove that the macroscopic dynamics of the system is correctly described by the time-dependent Gross-Pitaevskii equation, a cubic nonlinear Schroedinger equation for the wave function of the condensate.
   
Number Theory Seminar
Topic: Modular Units
Presenter: Amanda Folsom, UCLA
Date:  Friday, May 26, 2006, Time: 3:00 p.m., Location: Fine Hall 214
Abstract: In this talk I will discuss a particular family of modular units constructed using functional solutions to q-difference equations found in the work of Selberg. Arising in this way, these objects are of interest for various analytic properties and combinatorial interpretations. Dually, we exhibit fundamental algebraic roles played by these modular units, including those within the modular function fields, the modular unit groups, the cuspidal divisor class groups, class field theory, and the cyclotomic theory.