I will start by presenting some applications of the minimal model program to the construction of symplectic compactifications of certain Lagrangian fibrations (integrable systems) of geometric origin. One such case is that of the intermediate Jacobian fibration associated to a cubic fourfold (Donagi-Markman integrable system). In the second part of the talk, I will discuss aspects of the birational geometry of this fibration (e.g. the Mordell-Weil group).
Further information is available on the event page on the Indico platform.