Day 1 (Tuesday 11 April) @ 13:45–15:15
Olga Lukina (Leiden University)
Arboreal representations of Galois groups and Cantor dynamics
Arboreal representations of absolute Galois groups of number fields are given by groups of automorphisms of regular rooted trees, with the geometry of the tree determined by a polynomial which defines such a representation. Thus arboreal representations give rise to dynamical systems on a Cantor set, and are naturally a topic at the intersection of number theory, topological dynamics and geometric group theory. In the talk, I will briefly explain the construction of an arboreal representation, and how the fixed point properties of the action it defines are related to the questions about density of primes in certain non-linear recurrence relations. I will also give a brief overview of my recent results on classification of arboreal representations using invariants of topological dynamics, and of joint results with Maria Isabel Cortez on the properties of Frobenius elements under arboreal representations, in relation to the conjecture by Boston and Jones.