11 papers
The inverse Galois problem of iterated Galois groups and their fixed-point proportion
Santiago Radi
In 1985, Odoni initiated the study of arboreal representations and the fixed-point proportion, motivated by prime density problems in arithmetic dynamics. Since then, many question…
Proportion of periodic points in reduction of polynomials
Santiago Radi
In 2014, Juul, Kurlberg, Madhu and Tucker asked the following: given a number field and a rational function with coefficients in , if denotes the reduct…
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.
Branch iterated Galois groups with positive fixed-point proportion and positive Hausdorff dimension
Santiago Radi
In this article we prove that the arithmetic profinite iterated monodromy group of a post-critically infinite unicritical polynomial is regular branch (and so of positive Hausdorff…
Fixed-point proportion of geometric iterated Galois groups
Jorge Fariña-Asategui, Santiago Radi
In 1980, Odoni initiated the study of the fixed-point proportion of iterated Galois groups of polynomials motivated by prime density problems in arithmetic dynamics. The main goal…
Groups of finite type: classification and structural properties
Santiago Radi
Groups of finite type (also called finitely constrained groups), introduced by Grigorchuk, are known to be the closure of regular branch groups. This article explores many of their…
Random subgroups of branch groups
Jorge Fariña-Asategui, Santiago Radi
We show that independent Haar-random elements in a super strongly fractal branch profinite group generate a free subgroup acting freely on the boundary of the tree. This improves a…
A just-infinite iterated monodromy group without the congruence subgroup property
Santiago Radi
We prove that the iterated monodromy group of the polynomial is just-infinite, regular branch and does not have the congruence subgroup property. This yields the first exam…
On the fixed-point proportion of self-similar groups
Jorge Fariña-Asategui, Santiago Radi
We prove that super strongly fractal groups acting on regular rooted trees have null fixed-point proportion. In particular, we show that the fixed-point proportion of an infinite f…
A family of level-transitive groups with positive fixed-point proportion and positive Hausdorff dimension
Santiago Radi
This article provides a method to calculate the fixed-point proportion of any iterated wreath product acting on a -regular tree. Moreover, the method applies to a generalization…
Torsion elements in branch pro- groups
Jorge Fariña-Asategui, Santiago Radi
We show that the set of torsion elements of a topological group admitting a branch pro- quotient has Haar measure zero.