Galois theory of Dynamical Belyi Maps

Abstract: Let $f: \mathbb{P}^1_K \rightarrow \mathbb{P}^1_K$ be a rational map defined over a number field $K$. The Galois theory of the iterates $f^n=f \circ \dots \circ f$ has applications both in number theory and arithmetic dynamics. In this talk, we will discuss the various Galois groups attached to the iterates of $f$, namely arithmetic and geometric monodromy groups and Arboreal Galois representations. While providing a survey of recent results on the subject, we will also talk about joint work with I. Bouw and V. Karemaker on Dynamical Belyi maps.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

We normally meet in-person in the indicated room. For online editions, we use Zoom and distribute the link through the mailing list. If you wish to be put on the mailing list, please subscribe to ntag-external using lists.sfu.ca