Аннотация:
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.