# Mathematics Colloquia and Seminars

Consider a system of $N$ bosons interacting via a repulsive short range pair potential. Let $\psi_{N,t}$ be the solution to the Schrödinger equation of the N-particle dynamics. We prove that the one-particle density matrix of $\psi_{N,t}$ solves the time-dependent Gross-Pitaevskii equation, a cubic non-linear Schrödinger equation. We shall also review general problems related to quantum dynamics of N particle systems.