This short survey is part of a minicourse I gave during the CMI-HIMR Summer School
“Unlikely Intersections in Diophantine Geometry” on the Zilber–Pink conjecture, formulated …

Recent developments on the uniformity of the number of rational points on curves and
subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy …

Let's fix a complex abelian scheme endowed with a non-torsion section and with a finite
surjective modular map onto a universal family of abelian varieties (with some fixed level …

This note is a compte-rendu of my talks at the conference “Degeneracy of Algebraic Points”
in Spring 2023 at the SLMath (previously known as the MSRI) and at the ICCM 2023. It aims …

For each integer $ d\geq 2$, let $ M_d $ denote the moduli space of maps $ f:\mathbb {P}^
1\to\mathbb {P}^ 1$ of degree $ d $. We study the geometric configurations of subsets of …

We study the dynamics of algebraic families of maps on $\mathbb {P}^ N $, over the field
$\mathbb {C} $ of complex numbers, and the geometry of their preperiodic points. The goal …

In this paper, we establish the following family version of Habegger's bounded height
theorem on abelian varieties: a locally closed subvariety of an abelian scheme with Gao's …

Given an algebraic family $ f\colon\Lambda\times\mathbb {A}^ 2\to\Lambda\times\mathbb
{A}^ 2$ of plane polynomial automorphisms of H\'enon type parameterized by a quasi …

We study the dynamics of algebraic families of maps on Pn, over the field C of complex
numbers, and the geometry of their preperiodic points. The goal of this note is to formulate a …