Ljudmila Kamenova (University of NY at Stony Brook) will speak in the geometry seminar on 8th December 2015. The talk will be at 3.15pm in the Salle de Profs on the 9th floor of building NO. **Please note the unusual time** which is because there are two geometry seminars on the 8th December. Ljudmila’s title is *On Kobayashi’s pseudometric of compact complex manifolds.* The abstract follows.

The Kobayashi pseudometric on a complex manifold M is the maximal pseudometric such that any holomorphic map from the Poincare disk to M is distance-decreasing. Kobayashi conjectured that this pseudometric vanishes on Calabi-Yau manifolds. Using ergodicity of complex structures, together with S. Lu and with M. Verbitsky we prove this conjecture for all K3 surfaces and for most classes of hyperkahler manifolds. Another recent result which I will mention in the talk is that the existence of an infinite order automorphism of a compact complex manifold implies that the Kobayashi pseudometric is everywhere degenerate (this is joint with F. Bogomolov, S. Lu and M. Verbitsky).