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 seminar and workshops, and publications.
Recent Activity
My RIMS webpage contains further information on present seminar and daily activity.
- Talk :: Grothendieck's approach to Mathematics - Chapman Uni. US, (24-28.05.2022)
- Report :: Homotopic and Geometric Galois Theory in Oberwolfach (2021).
- Conference :: Homotopic and Geometric Galois Theory in Oberwolfach (2021).
- Talk :: DMV Annual Meeting 2020, ``Differential and Hodge Theoretic Methods in Algebraic Geometry'' Minisymposium, in Chemnitz, Germany (09.2020);
- Seminar :: RIMS - Homotopical Arithmetic Geometry Seminar - 7 Topics - 七福話 (May 2020 - Oct. 2020);
- Talk :: 5th KTGU Mathematics, RIMS Kyoto, Japan (02.07);
- Talk :: Algebra Seminar, Hiroshima University, Japan (01.2020);
- Talk :: Algebraic Number Theory and Related Topics Conference, at the RIMS Kyoto, Japan (12.2019);
- Talk :: Number Theory Seminar, at Kyoto University, Japan (8.11.2019);
- Seminar :: RIMS - Homotopical Anabelian Geometry Seminar (Nov. 2019 - March 2020);
- Position :: RIMS invited researcher, at RIMS Kyoto University, Japan (>7.09.2019);
- Talk :: Moduli stacks of curves: arithmetics and motives, at NTNU, Norway (08.2019);
- Talk :: Galois Arithmetic of Perverse Sheaves in genus 1, at XXIXèmes Rencontres Arithmétiques de Caen: ``Field Arithmetic and Arithmetic Geometry'' (29.05 -03.06.2019);
- Workshop :: Bayerische AG "Towards Chromatic Homotopy Theory"; incl. talk on ``Landweber Exact Functor Theorem: MU, Stack inertia & flatness'' (03.03.2019).
See here for more talks by topics, or here for organization of conferences and seminars, and here for international invitations.