Géométrie Arithmétique Effective à Clermont (GAEC)

ANR-23-CE40-0006-01  Axe F.1 Mathématiques (AAPG 2023)

 

Project abstract

The arithmetic geometry team of Clermont-Ferrand was born about twenty years ago and it has gradually developed to currently reach several (associate-)professors with various but related fields of expertise, ranging from Diophantine geometry to modular forms, including analytic number theory, modular curves and Galois representations. A common denominator of the work of the members of the group is the attention paid to effective and even explicit statements, which involve the natural invariants of the mathematical objects considered, with sometimes the use of machine calculations. The project aims to develop these effective aspects by strengthening the human potential of the team by recruiting a doctoral student, whose task is to study the notion of Siegel fields of functions and the geometry of numbers of rigid adelic spaces on these fields, as well as postdoctoral researchers who can work on the arithmetic of abelian varieties or Diophantine equations. This project is the opportunity to offer the arithmetic geometry team of Clermont-Ferrand a stronger cohesion and a greater international influence, consecrated by an end-of-project conference.

Members

Nicolas Billerey,  Éric Gaudron (scientific coordinator),  Richard Griffon,   François Martin,  Marusia Rebolledo,  Emmanuel Royer

Since February 1st, 2024, Florian Tilliet has joined our project team as a doctoral student.

Publications

1. Nicolas Billerey et al., On Darmon's program for the generalized Fermat equation, I (2024)  hal-04421240
2. Nicolas Billerey et al., On Darmon's program for the generalized Fermat equation, II (2024)  hal-04421243
3. Nicolas Billerey, Introduction to the modular method (2024)  hal-04421125
4. Éric Gaudron, Adelic approximation on spheres (2023)  hal-04507592

This research was funded in whole or in part by the French National Research Agency (ANR) under the ANR-23-CE40-0006-01 project. With the aim of its open access publication, the authors apply a CC BY open access license to any article or manuscript accepted for publication as a result of this submission.