Arithmetic & Homotopic Galois Theory
The LPP-RIMS Arithmetic & Homotopic Galois Theory IRN (AHGT) is a CNRS France-Japan International Research Network between Lille University (Laboratoire de Mathématiques Paul Painlevé), École Normale Supérieure - PSL (Département de Mathématiques et Applications), and the Research Institute for Mathematical Sciences, Kyoto University.
AHGT News & Activities
| Nov 16, 2025 | Workshop ``AHGT Days in Paris 2025'' , Sept. 23-24, 2024 |
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| Sep 26, 2025 | Atelier de Géométrie Arithmétique - 数論幾何学のアトリエ - , Septembre 26, 2025 |
AHGT Seminar
| Sep 8, 2025 | Anabelian properties of tame fundamental groups of singular curves. Murotani Takahiro (Kyoto Institute of Technology, Japan) |
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| Jul 7, 2025 | Automorphism groups of field extensions and the minimal ramification problem. Alexei Entin (Tel-Aviv University, Israel) |
Research Topics
The scientific activity of the AHGT IRN is structured around the 3 following topics and their interactions:
AHGT references
- Surveys & lectures notes, for a first contact with AHGT;
- Publications & preprints, per year and topic;
- ``Atelier Géométrie Arithmetic'' (notes), report on the young researches seminar.
- Galois Covers and Moduli Spaces. On the arithmetic of Hurwitz spaces, and Noether's program -- that originate in the Inverse Galois Problem -- and on Ihara's program that draw a bridge between number theory, motivic theory, and anabelian geometry [2024]:: [2023];
- Motivic & Geometric Galois Representations. Étale cohomology theory, Galois Representations theory, and Perverse sheaves theory are fully integrated and bring their complementary techniques with a richer derived spectrum [2024]:: [2023];
- Arithmetic Anabelian Geometry. Beyond Grothendieck's anabelian reconstruction program (and the section vs rational point issue), includes new minimality or ``close-to-anabelian'', and combinatorial arithmetic geometry approaches for new connections with Hurwitz spaces and Grothendieck-Teichmüller theory [2024]:: [2023];
Members & Research Partners
The network regroups the activity of around 60 researchers in France and in Japan, and is supported by 40 international researchers over 12 countries and 32 institutions.
Institutional Partners
