On the Morrison-Kawamata cone conjecture

If X is a Calabi-Yau manifold, then an important conjecture by Morrison and Kawamata predicts that the nef and mobile cones have a particularly nice desription in terms of actions of the groups Aut(X) and Bir(X). The conjecture has been verified for surfaces, and only in a small number of higher dimensional cases. In this talk, I will show how a certain version of the conjecture is true on Calabi-Yau 3-folds with Picard number 2, using a recent result of Oguiso. This is a joint work in progress with Thomas Peternell.