Hyperbolicity of Generic High-Degree Hypersurfaces

We will talk about the solution of the decades-old problem of the hyperbolicity of generic hypersurfaces of sufficiently high degree and of their complements, as well as a number of related results, such as:

• (i) a Big-Picard-Theorem type statement concerning extendibility, across the puncture, of holomorphic maps from a punctured disk to a generic hypersurface of high degree,
• (ii) entire holomorphic functions satisfying polynomial equations with slowly varying coefficients,
• (iii) Second Main Theorems for jet differentials and slowly moving targets.