DeMarco, Krieger, and Ye conjectured that there is a uniform bound B, depending only on
the degree d, so that any pair of holomorphic maps II: Écart uniforme entre Lattès et …

Point-counting results for sets in real Euclidean space have found remarkable applications
to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink …

In this paper, we prove that the admissible canonical bundle of the universal family of curves
is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for …

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 …

We prove that Zhang's dynamical Bogomolov conjecture holds uniformly along $1 $-
parameter families of rational split maps and curves. This provides dynamical analogues of …

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 …

We propose a formulation of the relative Bogomolov conjecture and show that it gives an
affirmative answer to a question of Mazur's concerning the uniformity of the Mordell–Lang …

Bogomolov and Tschinkel ['Algebraic varieties over small fields', Diophantine Geometry, U.
Zannier (ed.), CRM Series, 4 (Scuola Normale Superiore di Pisa, Pisa, 2007), 73–91] proved …

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 …