Abstract : The talk will present a complete Lipschitz classification of complex sur-face germs for the outer metric. It is based on the classification relative to the inner metric obtained 10 years ago with Lev Birbrair and Walter Neu-mann and on new tools involving non archimedean geometry, in particular the non-archimedean link which is a generalization of the valuative tree introduced by Favre and Jonsson, and ultrametrics on what we call the log-arithmic link of the singularity. This is a joint work with Lorenzo Fantini and Walter Neumann.

Keywords : Lipschitz homeomorphism; outer Lipschitz geometry; logarithmic link; complex surface singularity