Seminar in Real and Complex Geometry

Tuesday, 21.07.2015, 16:00-17:00, Schreiber building, room 209

Mikhail Verbitsky, High School of Economics

Proof of Morrison-Kawamata cone conjecture for hyperkahler manifolds


Morrison-Kawamata cone conjecture is a conjecture about the shape of an ample cone of a Calabi-Yau manifold. Morrison and Kawamata predicted that it is a polyhedron and the automorphism group acts on its faces with finitely many orbits. For hyperkahler manifolds it is proven; the proof is based on a result of hyperbolic geometry which is deduced from the Ratner theory of ergodic action on homogeneous spaces. I will tell the general scheme of the proof and explain how Ratner theory fits into the picture. This is a joint work with Ekaterina Amerik.