# Events

The Maseeh Mathematics and Statistics Colloquium Series*

presents

### Jamie Juul, Ph.D.

University of British Columbia

**Arboreal Galois Representations**

**Abstract: **

The main questions in arithmetic dynamics are motivated by analogous classical problems in arithmetic geometry, especially the theory of elliptic curves. We study one such question, which is an analogue of Serre's open image theorem regarding ℓ-adic Galois representations arising from elliptic curves. We consider the action of the absolute Galois group of a field on pre-images of a point α under iterates of a rational map f (that is, points that eventually map to α as we apply f repeatedly). These points can be given the structure of a rooted tree in a natural way. This determines a homomorphism from the absolute Galois group of the field to the automorphism group of this tree, called an arboreal Galois representation.

**Bio:**

I am a postdoctoral fellow at the University of British Columbia, working with Dragos Ghioca. I will start a position as an assistant professor at Colorado State University in fall 2020. Before I came to UBC, I was a visiting assistant professor at Amherst College 2015-2018. I received my Ph.D. in 2015 from the University of Rochester under the direction of Thomas J. Tucker. My research interests include arithmetic dynamics and algebraic number theory. My dissertation explored "Galois groups of iterated rational maps and their applications".

**Friday, November 22, 2019 at 3:15pm
Fariborz Maseeh Hall room B128
1855 SW Broadway
Light refreshments served**

The faculty host of this speaker is Dr. Derek Garton