Research interests :

Arithmetic geometry

Publications et prepublications

* Maximal slope of tensor product of Hermitian vector bundles, (.pdf).
      Journal of algebraic geometry 18 (2009), no. 3, 575-603.

* Harder-Narasimhan categories, (.pdf).
      Journal of pure and applied algebra 214 (2010), no. 2, 187-200.

* Convergence des polygones de Harder-Narasimhan, (.pdf). 
      Mémoires de la Société Mathématique de France 120 (2010), 1-120.

* Arithmetic Fujita approximation, (.pdf).
      Annales Scientifiques de l'École Normale Supérieure 43 (2010), no. 4, 555-578.

* (With S. Boucksom) Okounkov bodies of filtered linear series (.pdf).
      Compositio Mathematica 147 (2011), no. 4, 1205-1229.

* Differentiability of the arithmetic volume function (.pdf).
      Journal of the London Mathematical Society 84 (2011), no. 2, 365-384.

* Algebraicity of formal varieties and positivity of vector bundles (.pdf).
      Mathematische Annalen 354 (2012), no. 1, 171-192.

* Explicit uniform estimation of rational points I. Estimation of heights (.pdf).
      Journal für die reine und angewandte Mathematik 668 (2012), 59-88.

* Explicit uniform estimation of rational points II. Hypersurface coverings (.pdf).
      Journal für die reine und angewandte Mathematik 668 (2012), 89-108.

* (With J.-B. Bost) Concerning the semi-stability of tensor products in Arakelov geometry (.pdf).
       Journal des Mathématiques Pures et Appliquées 99 (2013), no. 4, 436-488.

* Fonction de Seshadri arithmétique en géométrie d'Arakelov (.pdf).
       Annales de la Faculté des Sciences de Toulouse 23 (2014), no. 3 (numéro spécial en l'honneur de C. Soulé), 561-590.

* Majorations explicites de fonctions de Hilbert-Samuel géométrique et arithmétique (.pdf).
       Mathematische Zeitschrift 279 (2015), no.1, 99-137.

* (With C. Maclean) Distribution of logarithmic spectra of the equilibrium energy (.pdf).
      Manuscripta Mathematica 146 (2015), no.3, 365-394.

* (With A. Moriwaki) Algebraic dynamical systems and Dirichlet's unit theorem on arithmetic varieties (.pdf).
      International Mathematical Research Notices 2015 (2015), no.24, 13669-13716.

* Inégalité d'indice de Hodge en géométrie et arithmétique : une approche probabiliste (.pdf).
       Journal de l'École Polytechnique - Mathématiques 3 (2016), 231-262.

* (With A. Moriwaki) Extension property of semipositive invertible sheaves over a non-archimedean field (.pdf).
       Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V, 18 (2018), no. 1, 241-282.

* Sur la comparaison entre les minima et les pentes (.pdf).
       Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2018 (2018), 5-23.

* On isoperimetric inequality in Arakelov geometry (.pdf).
       Bulletin de la Société Mathématique de France 146 (2018), no.4, 649-673.

* Okounkov bodies: an approach of function field arithmetic (.pdf).
      Journal de théorie des nombres de Bordeaux 30 (2018), no. 3, 829-845.

* (With A. Moriwaki) Arakelov geometry over adelic curves (.pdf). Errata.
      Lecture Notes in Mathematics 2258, Springer Singapore, 2020, xviii+452pp.

* (With H. Ikoma) On subfiniteness of graded linear series (.pdf).
      European Journal of Mathematics 6 (2020), no. 2, 367-399.

* (With A. Moriwaki) Arakelov theory on arithmetic surfaces over a trivially valued field (.pdf).
      International Mathematical Research Notices (2023), no. 7, 5473-5537.

* (With A. Moriwaki) Arithmetic intersection theory over adelic curves (.pdf).
      Mémoires de la Société Mathématique de France, to appear

* (With A. Moriwaki) Positivity in Arakelov geometry over adelic curves (.pdf).
       Progress in Mathematics 355, Birkhäuser, 2024, vii+253 pages.

* (With M. Jeannin) Harder-Narasimhan games (.pdf).       

Conference proceedings and unpublished texts

* Positive degree and arithmetic bigness (.pdf), 2008.
      
* Computing the volume function on a projective bundle over a curve (.pdf).
      RIMS Kôkyûroku 1745 (2011), 169-182.

* The applications of Okounkov bodies to arithmetic problems (.pdf).
      Oberwolfach report 11(2014), no.2, 1473-1477.

* Arithmetic approach to Newton-Okounkov bodies (.pdf).
       代数幾何学シンポジウム記録　(2018), 68-75.

* Comparison of some invariants of Euclidean lattices (.pdf).
       Proceedings of ICCM 2019.

* Introduction aux théorèmes de Hilbert-Samuel arithmétiques, (.pdf).
       Arakelov geometry and Diophantine applications, Chapter III, Lecture Notes in Mathematics 2276, Springer Cham, 2021, pp. 77-103.

* 丢番图问题, Arakelov 几何与凸几何, (.pdf).
       数学所讲座 2019

* (With A. Moriwaki) Sufficient conditions for the Dirichlet property (.pdf).       

Translation

Translation into Chinese of the book Introduction à la théorie analytique et probabiliste des nombres written by Gérald Tenenbaum
Table of Contents (目录)
The Chinese version 《解析与概率数论导引》 was published in a series of mathematical works "法兰西数学精品译丛" by Higher Education Press.

Doctoral and habilitation thesis

* Positivité en géométrie algébrique et en géométrie d'Arakelov (.pdf),
      Thèse de doctorat, École Polytechnique, Décembre 2006.

* Géométrie d'Arakelov: théorèmes de limite et comptage des points rationnels (.pdf),
     Habilitation à Diriger des Recherches, Université Paris Diderot, Décembre 2011.