R. Benedetto

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math.NT2025

Arboreal Galois groups of postcritically finite quadratic polynomials: The strictly preperiodic case

Robert L. Benedetto, Dragos Ghioca, Jamie Juul +1

In a previous paper, we provided an explicit description of the arboreal Galois group of the postcritically finite polynomial $f (z) = z^{2} + c$ in the special case when the critical…

math.NT2025

Arboreal Galois groups of postcritically finite quadratic polynomials: The periodic case

Robert L. Benedetto, Dragos Ghioca, Jamie Juul +1

We provide an explicit construction of the arboreal Galois group for the postcritically finite polynomial $f (z) = z^{2} + c$ , where $c$ belongs to some arbitrary field of characterist…

math.NT2025

The non-unit conjecture for Misiurewicz parameters

Robert L. Benedetto, Vefa Goksel

A Misiurewicz parameter is a complex number $c$ for which the orbit of the critical point $z = 0$ under $z^{2} + c$ is strictly preperiodic. Such parameters play the same role as special…

math.NT2024

Arboreal Galois groups for quadratic rational functions with colliding critical points

Robert L. Benedetto, Anna Dietrich

Let $K$ be a field, and let $f \in K (z)$ be rational function. The preimages of a point $x_{0} \in P^{1} (K)$ under iterates of $f$ have a natural tree structure. As a result, the Galois…