The work of Walter Bergweiler in value distribution of meromorphic functions

This is a colloquium talk in CAU, Kiel delivered on June 7, 2024 on the occasion of Walter Bergweiler’s retirement. Walter’s work on meromorphic functions consists of two parts: generalizations of Picard’s theorem to differential polynomials, and the applications of the rescaling principle known as the Bloch Principle. Since the talk was aimed at the general audience, a brief introduction to Nevanlinna theory is included.