## Arithmetic Homotopy Geometry

**Arithmetic Homotopy Geometry** at RIMS -- seminars, workshops, talks -- in collaboration and with the support of my RIMS colleagues (esp. Prof. Tamagawa, Mochizuki, Hoshi, Tsujimura, Minamide, Sawada).

Personal interest in the moduli stacks of curves and its stack inertia stratification — see for a glimpse; Includes simplical and homotopical algebraic geometry — i.e. model categories and motivic considerations for stacks à la *Morel-Voevodsky* —, the *arithmetic 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 —, the *arithmetic of operads* — in genus 0 via Friedlander étale topological type and prospaces, and the *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 references and publications.

### Homotopic Arithmetic Geometry - Seminars and Workshops

The **Arithmetic and Homotopic Galois Theory Seminar** is a monthly international hybrid seminar on the *latest developments of the AHGT project* [Link].

The **RIMS - Homotopic Arithmetic Geometry Seminars Series** is a RIMS seminar to introduce *key results of classical arithmetic geometry* in relation with recently developed techniques and principles (incl. a special session ``Promenade in Inter-universal Teichmüller theory'' with Lille University, France) [Link].

The Oberwolfach workshops series (2018, 2021, 2023) presents the latest international developments of the field and investigates new research directions.

## Recent Events

## Selected Talks & Activities

- The 22nd Affine Algebraic Geometry Meeting, Niigata (1 - 3.03.24)
*Géométrie arithmétique anabélienne, un panorama*, AHGT Seminar at ENS PSL, France (16.10.23);- Grothendieck's approach to Mathematics - Chapman Uni. US (24-28.05.22)
- Annual Meeting of the German Mathematic Association 2020 (DMV),
*``Differential and Hodge Theoretic Methods in Algebraic Geometry'' Minisymposium*, in Chemnitz, Germany (09.20); - 5th KTGU Mathematics, at RIMS Kyoto, Japan (02.07.20);
- Algebraic Number Theory and Related Topics, at RIMS Kyoto, Japan (12.19);
*Moduli stacks of curves: arithmetics and motives*, at NTNU, Norway (08.19);*Galois Arithmetic of Perverse Sheaves in genus 1*, at XXIXèmes Rencontres Arithmétiques de Caen: "Field Arithmetic and Arithmetic Geometry" (06.19);*"Landweber Exact Functor Theorem: MU, Stack inertia & flatness''*& org. of the Bayerische AG "Towards Chromatic Homotopy Theory" (03.19).*Arithmetic of Operads of Moduli Spaces of Curves*, at Temple University, US (03.18);- Homotopy Theory and Algebraic Geometry, SPP1786 Annual Meeting, Germany (03.17)

### Homotopical Arithmetic Geometry of Stacks - RIMS 2018

Moduli stacks of curves are ideal spaces in the study of geometric Galois representations and motivic theory. In these series of lectures, we present fundamental geometric and arithmetic properties of these spaces -- *I & II - Algebraic & Deligne-Mumford Stacks, III - Moduli Problems & Moduli Spaces of Curves, IV - Fundamental Group & Arithmetic, V - Motivic Theory for Moduli Stack of Curves* -- the goal being to introduce some elements of arithmetic homotopy theory (etale homotopy type, homotopical stacks, Morel-Voevodsky motivic homotopy).

*For details see RIMS - Number Theory / Arithmetic Geometry Seminar and Programme for references.*