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Height of rational points on algebraic varieties

Applicant Le Boudec Pierre
Number 170565
Funding scheme SNSF Professorships
Research institution Fachbereich Mathematik Departement Mathematik und Informatik Universität Basel
Institution of higher education University of Basel - BS
Main discipline Mathematics
Start/End 01.09.2017 - 31.08.2021
Approved amount 1'144'648.00
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Keywords (2)

Analytic Number Theory; Diophantine Geometry

Lay Summary (French)

Lead
Mon programme de recherche se situe à l'interface entre la Théorie Analytique des Nombres et la Géométrie Diophantienne.
Lay summary

Mon principal objectif est d'étudier divers problèmes concernant les points rationnels et les points entiers sur les variétés algébriques en utilisant des techniques de théorie analytique des nombres.
Direct link to Lay Summary Last update: 25.05.2017

Responsible applicant and co-applicants

Employees

Publications

Publication
Height of rational points on random Fano hypersurfaces
Le Boudec Pierre (2021), Height of rational points on random Fano hypersurfaces, in Algebra & Number Theory, 15(3), 657-672.
A statistical view on the conjecture of Lang about the canonical height on elliptic curves
Le Boudec Pierre (2019), A statistical view on the conjecture of Lang about the canonical height on elliptic curves, in Transactions of the American Mathematical Society, 1.

Collaboration

Group / person Country
Types of collaboration
Tim Browning, IST Austria Austria (Europe)
- in-depth/constructive exchanges on approaches, methods or results
- Publication
Will Sawin, Columbia University United States of America (North America)
- in-depth/constructive exchanges on approaches, methods or results
- Publication

Scientific events

Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
9th swiss-french workshop in Algebraic Geometry Talk given at a conference The Hasse principle and random Fano hypersurfaces 13.01.2020 Charmey, Switzerland Le Boudec Pierre;
Antrittsvorlesung Individual talk Random Diophantine equations 12.12.2019 Universität Basel, Switzerland Le Boudec Pierre;
Séminaire de Théorie des Nombres Individual talk Le principe de Hasse pour les équations diophantiennes aléatoires 22.11.2019 Université de Bordeaux, France Le Boudec Pierre;
Groups, Arithmetic and Algebraic Geometry Seminar Individual talk The Hasse principle for random Diophantine equations 29.10.2019 Ecole Polytechnique Fédérale de Lausanne, Switzerland Le Boudec Pierre;
Rational points on Fano and similar varieties, Institut Henri Poincaré Talk given at a conference On a conjecture of Poonen and Voloch: Lattice point counting and the variance of the number of rational points on Fano hypersurfaces 21.05.2019 Paris, France Le Boudec Pierre;
Seminar of the trimester Reinventing rational points, Institut Henri Poincaré Individual talk A statistical version of a conjecture of Lang 16.05.2019 Paris, France Le Boudec Pierre;
Number Theory Seminar, Université Clermont Auvergne Individual talk Elliptic curves with large Tate-Shafarevich groups 05.03.2019 Clermont-Ferrand, France Griffon Richard;
Algebra and Number Theory Seminar, Université de Franche-Comté Individual talk Elliptic curves with large Tate-Shafarevich groups 05.02.2019 Besançon, France Griffon Richard;
AIMS-Stellenbosch Number Theory 2019, Stellenbosch University Talk given at a conference Elliptic curves with large Tate-Shafarevich groups over function fields 14.01.2019 Stellenbosch, South Africa Griffon Richard;
Arithmetic and L-functions, Université de Franche-Comté Talk given at a conference Elliptic curves with large Tate-Shafarevich groups and Siegel's theorem 14.11.2018 Besançon, France Griffon Richard;
Algebraic Geometry and Number Theory Seminar, IST Austria Individual talk Height of rational points on random Fano hypersurfaces 11.10.2018 Vienna, Austria Le Boudec Pierre;
Mathematical Colloquium, Universität Bern Individual talk On the Hasse principle in families of Diophantine equations 24.09.2018 Bern, Switzerland Le Boudec Pierre;
Number Theory Seminar, Universität Basel Individual talk A statistical version of a conjecture of Lang 05.10.2017 Basel, Switzerland Le Boudec Pierre;


Self-organised

Title Date Place
Topics in Rational and Integral Points, Universität Basel 02.09.2019 Basel, Switzerland
Number Theory Seminar, Universität Basel 01.09.2017 Basel, Switzerland

Associated projects

Number Title Start Funding scheme
202664 Height of rational points on algebraic varieties 01.09.2021 SNSF Professorships

Abstract

My research program is at the interface between Analytic Number Theory and Diophantine Geometry. To be more specific, it mainly consists in using analytic number theory techniques to investigate quantitative aspects of rational and integral points on algebraic varieties.
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