2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127000We 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.20 pages, 2 figures; contribution to the Proceedings of the International Congress on Mathematical Physics held at IMPA in Rio de Janeiro in August 2006Mathematical Physics35Q55; 81Q15; 81T18; 81V70text