  In experiments, Bose-Einstein condensates are prepared by cooling a dilute
Bose gas in a trap. After the phase transition has been reached, the trap is
switched off and the evolution of the condensate observed. The evolution is
macroscopically described by the Gross-Pitaevskii equation. On the microscopic
level, the dynamics of Bose gases are described by the $N$-body Schr\"odinger
equation. We review our article [BdS12] in which we construct a class of
initial data in Fock space which are energetically close to the ground state
and prove that their evolution approximately follows the Gross-Pitaevskii
equation. The key idea is to model two-particle correlations with a Bogoliubov
transformation.
