Seminario Teoría de Números UAM-ICMAT

AN OVERVIEW ON ARBOREAL GALOIS REPRESENTATIONS


SPEAKER: Andrea Ferraguti (Max Planck Institute, Bonn)

DATE & TIME: Tuesday, 23rd July 2019 - 11:30

VENUE: Aula Gris 1, ICMAT

ORGANISER: UAM - ICMAT

Abstract: Arboreal Galois representations are central objects in modern arithmetic dynamics. They are defined as continuous homomorphisms, associated to rational maps over algebraic varieties, from the absolute Galois group of a field to the automorphism group of a special graph, and they are considered to be the dynamical avatars of Galois representations attached to Tate modules of abelian varieties. Due to their nature, they combine in a beautiful way several combinatorial, arithmetic and group-theoretic information. In this talk I will introduce them, showing peculiar examples and the most important conjectures around the topic. Afterwards, I will explain the ideas behind our recent proof of Jones' conjecture (joint with G. Micheli).