Arithmetic Homotopy Geometry - Seminars & Workshops
Arithmetic Homotopy Geometry - Seminars
The goal of the Homotopic Arithmetic Geometry Seminars Series is to introduce key results of classical arithmetic geometry in relation with recent developments of the field (e.g. simpicial homotopy theory). Semester '20-21 was a special session with Lille University (France) on IUT geometry; year '21-22 has been focused on the ``Expanding Horizons of IUT theory'' special year.
Since Jan. 2023, the seminar activity is now part of the ``AHGT Seminar'' of the LPP-RIMS AHGT International Research Network. See the page of each semester (left) for programmes, references, and list of participants.
Arithmetic Homotopy Geometry - Workshops
Homotopic and Geometric Galois Theory - Oberwolfach 2021
A fundamental idea in studying the absolute Galois group of a field is to make it act on geometric objects such as Galois covers, étale cohomology groups and fundamental groups. Striking advances have recently shed new light on the seminal topics of (a) Galois Covers, (b) Motivic Representations, and (c) Anabelian Geometry. Essential crossbridging principles connect these advances: homotopic methods, higher stacks, Tannakian symmetries. Based on the recent results and their promising connections, and on the 2018 MFO mini-workshop in a similar spirit, this workshop aims to crystallize these innovative approaches and to strengthen fruitful desire paths in homotopic and geometric Galois theory -- With P. Dèbes, H. Nakamura, and J. Stix.
RIMS - Expanding Horizons of Inter-universal Teichmüller Theory 2021-2022
Inter-universal Teichmüller theory can be seen as a new kind of geometry, which beyond Grothendieck's ring-scheme algebraic geometry, reunites seminal anabelian, arithmetic and Diophantine insights. The goal of this series of workshops (WS1-4) is to present techniques and principles of these theories in relation with the absolute Galois group of the rational numbers (and its GT combinatoric variant).
We refer to the official page of Prof. S.Mochizuki's project for further details on programme, dates, and participants of the Workshops WS1-WS4.
Arithmetic Geometry and Symmetries around Galois and Fundamental Groups - Oberwolfach 2018
The geometric study of the absolute Galois group of the rational numbers has been a highly active research topic since the first milestones: Hilbert’s Irreducibility Theorem, Noether’s program, Riemann’s Existence Theorem. It gained special interest in the last decades with Grothendieck’s “Esquisse d’un programme”, his “Letter to Faltings” and Fried’s introduction of Hurwitz spaces. It grew on and thrived on a wide range of areas, e.g. formal algebraic geometry, Diophantine geometry, group theory. The recent years have seen the development and integration in algebraic geometry and Galois theory of new advanced techniques from algebraic stacks, l-adic representations and homotopy theories. It was the goal of this mini-workshop, to bring together an international panel of young and senior experts to draw bridges towards these fields of research and to incorporate new methods, techniques and structures in the development of geometric Galois theory -- With P. Dèbes and M. Fried.