# Geometria em Lisboa Seminar

### 26/07/2018, 16:30 — 17:30 — Room P3.10, Mathematics Building

Bruno Oliveira, *University of Miami*

### Hyperbolicity of projective manifolds (II)

We continue to discuss several ideas and methods used in studying the Kobayshi hyperbolicity of projective manifolds. A manifold $X$ is said to be hyperbolic if there are no nonconstant holomorphic maps from the complex line to $X$. This is a subject that brings together methods of algebraic geometry, complex analysis and differential geometry.

We will discuss the key and well understood case of dimension $1$. We will have several distinct characterizations of hyperbolicity and see how that extend for projective manifolds of higher dimension. We will also discuss the related Green-Griffiths-Lang conjecture.

This is the second part of a two seminar set, but can be followed independently of the first seminar.