Abstract: The Cone conjecture of Morrison and Kawamata is a still mysterious prediction about the structure of the nef and movable cones on a
Calabi-Yau variety, and very little is known in dimensions at least 3.
In this talk I will present some motivation for the conjecture, and
discuss the proof of the conjecture for Calabi-Yaus with Picard number 2
and infinite group of birational automorphisms.

This is joint work with Thomas Peternell.