College of Liberal Arts & Sciences

# Differential Geometry Seminar

Speaker:

Ljudmila Kamenova（Stony Brook University）

Topic:

Non-hyperbolicity of hyperkähler manifolds and Kobayashi's conjectures

**Abstract: **

The Kobayashi pseudometric $d_M$ 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, and in particular, Calabi-Yau manifolds have "entire curves". Using ergodicity of complex structures, together with S. Lu and M. Verbitsky we prove this conjecture for all K3 surfaces and for many classes of hyperkähler manifolds.

Event Date:

April 27, 2021 - 10:30am to 11:20am

Location:

Online

Calendar Category:

Seminar

Seminar Category:

Differential Geometry