Arithmetic Homotopy Geometry
International activity and personnal contributions -- mainly on the moduli stacks of curves and their stack inertia stratification. Includes simplical and homotopical algebraic geometry — i.e. model categories and motivic considerations for stacks à la Morel-Voevodsky—, arithmetic anabelian geometry of curves — e.g. G-covers, irreducible components of Hurwitz spaces, étale fundamental group —, Grothendieck-Teichmüller theory — e.g. mapping class groups, pants decompositions, Serre bonté —, arithmetic of operads — in genus 0 via Friedlander étale topological type and prospaces—, and Tannakian formalism in Perverse sheaves.
Since 2023 this activity takes place in the CNRS France-Japan International Research Network LPP-RIMS ``Arithmetic & Homotopic Galois Theory'' (AHGT), see AHGT seminar and workshops, and AHGT publications.
- [Report] Arithmetic Homotopy and Galois Theory
- [RIMS] Arithmetic Homotopy Geometry
- [News] RIMS website
Activities (selection)
- Talk :: Homotopic Galois theory: arithmetic principles 22nd Affine Algebraic Geometry Meeting, Niigata Japan (1-3.03.2024)
- Workshop :: MFO-RIMS - Arithmetic Homotopy and Galois Theory (24-29.09 2023)
- Students :: In anabelian arithmetic geometry & topics [Link]
- Talk :: Géométrie arithmétique anabélienne, un panorama AHGT Seminar at ENS PSL, France (16.10.2023)
- Talk :: Grothendieck's approach to Mathematics - Chapman Uni. US, (24-28.05.2022)
- Talk :: DMV Annual Meeting 2020, ``Differential and Hodge Theoretic Methods in Algebraic Geometry'' Minisymposium, in Chemnitz, Germany (2020);
- Talk :: 5th KTGU Mathematics, RIMS Kyoto, Japan (2020);
- Seminar :: RIMS Arithmetic Homotopy Geometry (2019-...)
Manuscripts (selection)
- Paper :: On Oda's problem and special loci, submitted, 2023
- Paper :: Monodromy of Elliptic Curve Convolution, Seven-point sheaves of G2-type, and Motives of Beauville type, Crelles. 2021
- Paper :: On Galois Action on Stack Inertia of Moduli Spaces of Curves, Pub. RIMS, 2023
- Notes :: Seven Topics of Homotopic Arithmetic Geometry – 七福話, 2021
- Notes :: The Landweber Exact Functor Theorem (BAG), 2018
- Report :: Arithmetic and Homotopy of Moduli Stacks of Curves, MFO report, 2018