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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).