Abstract
Campana proposed a series of conjectures
relating algebro-geometric and complex-analytic properties of
algebraic varieties and their arithmetic. The main ingredient is
the definition of the class of special varieties, which is the
key for a new functorial classification of algebraic varieties,
that is more suitable to answer arithmetic questions. In the
talk we will review the main conjectures and constructions, and
we will discuss some recent results that give evidence for some
of these conjectures. This is joint work with E. Rousseau and J.
Wang.