Arithmetic and Diophantine Geometry, via Ergodic Theory and o-minimality

Session

Morning Chair: Hélène Esnault

8 sept. 2025, 09:15

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

2. The Arithmetic of Power Series and Applications to Irrationality

Yunqing Tang (Caltech & UC Berkeley)

08/09/2025 10:00

We will discuss a new approach to prove irrationality of certain periods, including the value at 2 of the Dirichlet L-function associated to the primitive quadratic character with conductor -3. Our method uses rational approximations from the literature and we develop a new framework to make use of these approximations. The key ingredient is an arithmetic holonomy theorem built upon earlier...

4. Integral Points and Affineness in Arakelov Geometry

François Charles (ENS Paris)

08/09/2025 11:15

I will describe results old and new regarding finiteness and infiniteness of integral points on arithmetic schemes, subject to analytic conditions. I will explain how the language of A-schemes and the use of theta-invariants, as developed in joint work with Bost, provides a geometric framework for this kind of questions, and how it relates to notions of affineness in Arakelov geometry.

1. Opening Address