3 papers
math.NT2026
2007: An Arboreal Odyssey: A View of Arboreal Galois Representations and Applications, from Early in the Subject's History
Rafe Jones
The study of arboreal Galois representations (that is, Galois groups arising from iteration of polynomial and rational functions) originated with work of Odoni in the 1980s. Beginn…
math.DS2026
Corrigendum and addendum to "Fixed-point-free elements of iterated monodromy groups" [Trans. of the American Mathematical Society Vol. 367, No. 3 (2015), 2023-2049]
Jorge Fariña-Asategui, Rafe Jones, Santiago Radi
In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.
math.NT2026
On the Arithmetic of Bicritical Rational Functions
Vefa Goksel, Rafe Jones
Bicritical rational functions -- those with precisely two critical points -- include the well-studied families of unicritical polynomials and quadratic rational functions. In this…