We report on some recent results concerning the dynamics of Bose-Einstein
condensates, obtained in a series of joint papers with L. Erdos and H.-T. Yau.
Starting from many body quantum dynamics, we present a rigorous derivation of a
cubic nonlinear Schroedinger equation known as the Gross-Pitaevskii equation
for the time evolution of the condensate wave function.Comment: 20 pages, 2 figures; contribution to the Proceedings of the
International Congress on Mathematical Physics held at IMPA in Rio de Janeiro
in August 200
