Abstract:
A linear connexion with 4 singular regular points induces by monodromy a representation of the fundamental group of the sphere  punctured by 4 points. If the connexion has irregular singular points we need to introduce "wild fundamental groupoid"s. I will present the construction of such groupoids , their representations and the morphisms between them. They define confluent morphisms between the corresponding character varieties. Our main result states that these morphisms are birational maps, which allows to define confluent dynamics on wild character varieties.