Algebraic and Arithmetic Geometry Seminar

Abelian dynamical Galois groups

by Andrea Ferraguti (SNS, Pisa)

Europe/Rome
Aula Seminari (Dipartimento di Matematica)

Aula Seminari

Dipartimento di Matematica

Description

Dynamical Galois groups are invariants associated to dynamical systems generated by the iteration of a self-rational map of $\mathbb{P}^1$. These are still very mysterious objects, and it is conjectured that abelian groups only appear in very special cases. We will show how the problem is deeply related to a dynamical property of these rational maps (namely that of being post-critically finite) and we will explain how to approach and prove certain non-trivial cases of the conjecture. This is based on joint works with A. Ostafe, C. Pagano and U. Zannier.