Atelier de Géométrie Arithmétique - 数論幾何学のアトリエ 2024
Around the Grothendieck-Teichmüller group
The Grothendieck-Teichmüller group GT, first introduced by Drinfel'd and Ihara in the 90s, follows Grothendieck's insight of ``Esquisse d'un programme'' to encapture the absolute Galois group of rational numbers in a combinatorial way, via topological group properties, within the outer automorphism group of a certain category of tower of étale fundamental groupoids. Recent breakthroughs were obtained, on the topological side (via operads, see Fresse-Horel ~2012) and on the arithmetic side (via combinatorial anabelian geometry, see Hoshi-Minamide-Mochizuki ~2017).
The goal of this workshop is to provide an arithmetical construction of the Grothendieck- Teichmüller group such as given by Ihara, and a practical understanding of the anabelian and geometric methods used by Hoshi, Minamide and Mochizuki to provide recent results on GT. We refer to the program for a description of talks and a list of references.
This atelier is organized with the support of the École Parisienne d'Arithmétique et de Géométrie (ÉPAG).
Next Atelier. Following the vote of the participants, the next atelier will be ``on perfectoid spaces''.
Participants
| Salim Alloun | ENS de Lyon - Sorbonne Université | Paris |
| Antonin Assoun | Université de Lille | Paris |
| Elias Caeiro | École Normale Supérieure PSL | Paris |
| Lucas Dauger | Sorbonne Université | Paris |
| Moulinier Enguerrand | Sorbonne University | Paris |
| Mattias Ferreira-filoramo | Sorbonne University Paris | Paris |
| Tokihiro Fushimi | RIMS Kyoto University | Kyoto |
| Yuki Goto | Keio University | Kyoto |
| Shun Ishii | Keio University | Kyoto |
| Kohei Kitamura | Osaka University | Kyoto |
| Antoine Klughertz | ENS de Lyon | Paris |
| Yuki Kondo | Osaka University | Kyoto |
| Kaiji Kondo | RIMS Kyoto University | Kyoto |
| Brieuc Lair | École Normale Supérieure PSL | Kyoto |
| Louis Loiseau | Université de Nantes | Paris |
| Maxime Lombard | Université de Nantes | Paris |
| Takahiro Murotani | Tokyo Institute of Technology | Kyoto |
| Hamza Oussama | Western University | Paris |
| Sabatin Owen | ENS Paris | Paris |
| Séverin Philip | RIMS Kyoto University | Kyoto |
| Wang Qixiang | Université Paris-saclay | Paris |
| Densuke Shiraishi | Osaka University | Kyoto |
| Jianbo Sun | Kyushu University | Kyoto |
| Reiya Tachihara | RIMS Kyoto University | Kyoto |
| Naoka Takada | Osaka University | Kyoto |
| Nikola Tomic | Université de Montpellier | Paris |
| Ayano Tsukimori | Nagoya university | Kyoto |
| Hidetada Wachi | Keio University | Kyoto |
| Shiyuan Wan | University of Bordeaux | Paris |
| Khalef Yaddaden | University of Nagoya | Kyoto |
| Naganori Yamaguchi | Tokyo Institute of Technology | Kyoto |
| Xiaodong Yi | Université de Lille | Paris |
| Adrien Zabat | Sorbonne Université | Paris |
The Atelier takes place in-person with a Zoom bridge between RIMS Kyoto and Paris. Participants proposes and vote for the next Atelier topic.
Organizers: M. Ferreira-Filoramo (France), S. Philip (RIMS JP) or N. Yamaguchi (Tokyo JP).