Ophelia Adams

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20212025

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math.NT2025

Semiconjugacy and Self-Similar Subgroups of pfIMGs

Ophelia Adams

The profinite iterated monodromy group (pfIMG) is a self-similar group associated to dynamical systems. We show that its proper open self-similar subgroups correspond to highly rig…

math.NT2025

Profinite Iterated Monodromy Groups of Unicritical Polynomials

Ophelia Adams, Trevor Hyde

Let $f (x) = a x^{d} + b \in K [x]$ be a unicritical polynomial with degree $d \geq 2$ which is coprime to $char K$ . We provide an explicit presentation for the profinite itera…

math.NT2022

A Dynamical Analogue of the Criterion of Néron-Ogg-Shafarevich

Ophelia Adams

We introduce an anabelian approach to the study of arboreal Galois representations and apply Tamagawa's anabelian version of the Néron-Ogg-Shafarevich criterion to produce a dynami…

math.NT2021

A Dynamical Analogue of Sen's Theorem

Ophelia Adams

We study the higher ramification structure of dynamical branch extensions, and propose a connection between the natural dynamical filtration and the filtration arising from the hig…