# Polynomial Dynamics over Number Fields

Alex Patterson

## Affiliation:

University of New South Wales

## Date:

Tue, 19/11/2019 - 12:00pm to 1:00pm

## Venue:

RC-4082, The Red Centre, UNSW

## Abstract:

Let $f$ be a polynomial over a field $F$ and let $f^{(n)}$ denote the $n$-th iterate of $f$. An active research area in the field of arithmetic dynamics is to investigate the properties of $f^{(n)}$for an arbitrary $n \in \mathbb{Z}_{\geq 1}$. In particular, this investigation focuses on questions of factorisation, and the behaviour of points under repeated application of $f$. We discuss problems of this type when $F$ is a number field and give a generalisation of previous work by Ahmadi, Luca, Ostafe and Shparlinski to the context of number fields.