Version françaiseCentre Émile Borel
Doctoral program on Diophantine Geometry
Rennes, June 14–26, 2009
Aims and scope
Diophantine geometry is the geometric study of diophantine equations. In the last 30 years, it has seen tremendous developments, including proofs of Mordell's conjecture by Faltings, Vojta and Bombieri, the invention of Arakelov geometry by Arakelov, Faltings, and Gillet–Soulé, and its use in transcendence theory and traditional diophantine approximation, the proof by Ullmo and Zhang of Bogomolov's conjecture, the new proof of Siegel's theorem by Kim, and the proof of Vojta's (1+ε)–conjecture over function fields by McQuillan and Yamanoi. The goal of this conference is to present these results to young master2 and PhD students, starting at the level of basic master courses in Algebraic geometry and Number theory and reaching those recent results.
The conference will run from Monday, June 15th to Friday, June 26th, with a break during the week-end so that the students can take profit of their stay in Bretagne.
There will be four lectures per day, one hour each, as well as a question&answers session. We will also organize presentations by the students themselves of their own research projects.
The lectures will be made in English or in French, according to the speakers and the participants, even though these web pages only give english titles. We will distribute lecture notes to the participants.
Lectures
- Marc Hindry (Université Paris 7 – Denis Diderot, France) : Arithmetic and geometry of curves and abelian varieties
- Antoine Chambert-Loir (Université de Rennes 1, France) : Arakelov Geometry, heights and the Bogomolov conjecture
- Michael Nakamaye (New Mexico University, United States) : The geometry of Roth's theorem
- Sinnou David (Université Paris 6 – Pierre et Marie Curie, France) : Diophantine approximation on Abelian varieties
- Yuri Bilu (Université Bordeaux 1, France) : The Schmidt subspace theorem and its recent applications
- Carlo Gasbarri (Università Roma 2, Italy) : Arithmetic geometry and the ABC conjecture on function fields
- Stefan Wewers (Leibniz Universität Hannover, Germany) : The non-abelian Chabauty method
