# Abelian dynamical Galois groups – Andrea Ferraguti (SNS, Pisa)

#### Venue

Dipartimento di Matematica, Aula Seminari.

#### Abstract

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.

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