Kobayashi Non-Hyperbolicity of Calabi-Yau Manifolds via Mirror Symmetry

Explore Kobayashi non-hyperbolicity of Calabi-Yau manifolds through the lens of mirror symmetry in this 56-minute Western Hemisphere Virtual Symplectic Seminar talk by Ljudmila Kamenova from Stony Brook University. Delve into the existence of entire curves on compact complex manifolds and discover how mirror symmetry techniques reveal elliptic or rational curves on Calabi-Yau manifolds with non-Hodge degenerate mirror duals. Examine key concepts including hyperkähler manifolds, Lagrangian fibrations, Kobayashi's pseudometric and conjectures, holomorphic Ray-Singer torsion, and the BCOV-FL formula. Investigate specific examples such as quintic threefolds and explore non-hyperbolicity results in various dimensions. Gain insights into this collaborative research with Cumrun Vafa, advancing our understanding of complex geometry and mirror symmetry.

Intro
Basics - Calabi-Yau
Examples of hyperkähler manifolds
Lagrangian Fibrations
Kobayashi's pseudometric
Kobayashi's conjectures
Main Theorems
Upper semicontinuity and double fibrations
Holomorphic Ray-Singer torsion
BCOV - FL formula
Relations in small dimensions
Quintic threefolds
Non-hyperbolicity results