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 …

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 …

The Torsion Anomalous Conjecture states that an irreducible variety $ V $ embedded in a
semi-abelian variety contains only finitely many maximal $ V $-torsion anomalous varieties …

A deep conjecture on torsion anomalous varieties states that if $ V $ is a weak-transverse
variety in an abelian variety, then the complement $ V^{ta} $ of all $ V $-torsion anomalous …

This thesis consists of six chapters and two appendices. The first two chapters contain the
introduction and some preliminaries. Chapter 3 contains a characterization of curves in …

In this article, we prove that the Zilber-Pink conjecture for abelian varieties over an arbitrary
field of characteristic $0 $ is implied by the same statement for abelian varieties over the …

Dans ce mémoire, je présente les recherches que j'ai menées au cours des dix dernières
années, depuis ma thèse jusqu'à aujourd'hui, sur certains problèmes en géométrie …

Let be a curve of genus at least 2 embedded in, where the. As a corollary, we give an explicit
bound for the height of the rational points of special curves, proving new cases of the explicit …

Mumford, conjecture de Zilber-Pink, géométrie diophantienne, géométrie tropicale,
hauteurs, intersections exceptionnelles, multiplication complexe, o-minimalité, problème de …

We give an overview of some landmark theorems and recent conjectures in Diophantine
Geometry. In the elliptic case, we prove some new bounds for torsion anomalous points and …