Prossimi seminari

Arboreal Galois representations are central objects in modern arithmetic dynamics. They are built from the iterations of a rational map of the projective line, and they encode in a beatiful way arithmetic, combinatorial and group-theoretic information about the absolute Galois group of a field. In this talk, we will recall the construction, the basic properties and some peculiar examples. Afterwards, we will explain the ideas behind our recent proof of Jones' conjecture, that allows to construct infinite families of geometrically surjective arboreal representations in any characteristic. The key ingredient is a new effective, uniform bound for the height of integral points on elliptic curves over global function fields. This is joint work with G. Micheli.