Clara Dérand

R. Nevanlinna's theory of value distribution of holomorphic mappings originates in the well-known theorem of Picard, which states that any transcendental entire function reaches all complex values infinitely often with at most one exception. The basic strategy of Nevanlinna theory consists in comparing several growth-measuring functions. I will describe the main results in one and several variables and mention various generalisations of the original framework. I will also try to explain some important consequences concerning hyperbolicity problems in complex geometry. If time permits, I will also mention the deep connections with some number theory questions as Diophantine approximation and the abc-conjecture.