Mochizuki's Inter-Universal Teichmüller theory provides a new geometry that brings within reach an estimate of certain rigidity property of isomorphisms intertwining the multiplicative and additive monoid structures of the natural numbers.

IUT geometry deals with the moduli stack of elliptic curves for capturing some rigid Diophantine properties of arithmetic line bundles in terms of some absolute mono-anabelian geometry deconstruction-reconstruction process -- or Fukugen 復元.

The goal of this seminar between Painlevé-Lille (France) and RIMS-Kyoto (Japan) — September 2020 - April 2021 — is for generic arithmetic-geometers to gain a general understanding of results, insights and techniques of IUT. It is organized around the three following topics:

• Diophantine Geometry. Abc & Szpiro conjectures: Roth's Theorem & Belyi - Abc & Vojta Conjectures: Heights & Ramification - From Vojta to Mochizuki: Moduli Spaces of Elliptic Curves.
• IUT Geometry. Hodge Theaters: Apparatus for Global Multiplicative Subspaces - Cyclotomic Rigidity & Multiradiality: LCF, coricity & Mono-theta Environments - Log-Theta Lattices & Symmetries: Indeterminacies, log-shell & Multiradiality.
• Anabelian Geometry. Relative Bi-anabelian Geometry: Towards mono-anabelian - Tempered Anabelian Geometry: Combinatorial Geometry - IUT Absolute: Mono-anabelian Reconstructions.

It is completed with talks on (1) Anabelian Geometry for IUT (Hoshi), (2) p-adic Teichmüller Theory (Wakabayashi), and (3) Q&A Session on Inter-Universal Teichmüller Theory (Mochizuki).

We refer to the Programme of the seminar as well as to the links below for further details and references on the theory.