Clay Mathematics Institute Workshop on IUT Theory of Shinichi Mochizuki

Symmetries and Correspondences - Forthcoming Conferences


December 7-11 2015 Oxford, Clay Mathematics Institute

Organizers: Ivan Fesenko, Minhyong Kim, Kobi Kremnitzer


Supported by Clay Mathematics Institute and Symmetries and Correspondences



The work (currently being refereed) of Shinichi Mochizuki on
inter-universal Teichmuller theory (arithmetic deformation theory) and
   its application to famous conjectures in diophantine geometry became
   publicly available in August 2012. This theory, developed over 20 years, introduces a vast collection of novel ideas, methods and objects.  Aspects of the theory extend arithmetic geometry to a non-scheme-theoretic setting and, more generally, have the potential to open new fundamental areas of mathematics. 
This workshop aims to present and analyse key principles, concepts, objects and proofs of the theory of Mochizuki and study its relations with existing theories in different areas, to help to increase the number of experts in the theory of Mochizuki and stimulate its further applications.


Shinichi Mochizuki will answer questions during two three hour skype sessions during the workshop. He also responds directly to emailed questions.


CMI page of the workshop

A version of this page with a picture

Mathematicians willing to participate in the workshop or having questions about its texts (whether or not attending the workshop) should first register an interest by sending answers to this questionnaire to symmetries.correspondences@gmail.com
To formally register to participate in the workshop use the CMI page for instructions how to do that and for other local information.


Senior participants include (*= to be confirmed)
A. Beilinson (Chicago), G. Faltings (Bonn), I. Fesenko (Nottingham), D. Goldfeld (Columbia Univ.), * Ch. Haesemeyer (Los Angeles), N. Hitchin (Oxford), Yu. Hoshi (Kyoto), * E. Hrushovski (Jerusalem), K. Kedlaya (San Diego), M. Kim (Oxford), K. Kremnitzer (Oxford), U. Kühn (Hamburg), * F. Loeser (Paris), Ch.P. Mok (Purdue Univ.), A. Schmidt (Heidelberg), J. Stix (Frankfurt), T. Szamuely (Budapest), F. Tan (Shanghai), D. Thakur (Rochester), * Yu. Tschinkel (New York), F. Voloch (Austin), B. Yalkinoglu (Strasbourg), Sir A. Wiles (Oxford), G. Yamashita (Kyoto), S.-W. Zhang (Princeton), B. Zilber (Oxford).

Younger participants include
A. Cruz Morales (Rio de Janeiro/Bonn), T. Dupuy (Los Angeles), A. Ivanov (München), A. Javanpeykar (Mainz), R. Kucharczyk (Bonn), L. Kuehne (Bonn), W. Czerniawska (Nottingham), J. Lim (Oxford), T. Oliver (Bristol), W. van Urk (Nottingham), M. Waller (Nottingham).


1st letter to participants of the workshop


Introductory and lecture notes texts:

Bogomolov's proof of the geometric version of the Szpiro conjecture from the point of view of inter-universal Teichmueller theory, by Shinichi Mochizuki

Invitation to inter-universal Teichmüller theory (lecture note version), by Shinichi Mochizuki

A panoramic overview of inter-universal Teichmüller theory, by Shinichi Mochizuki

On the verification of inter-universal Teichmüller theory: a progress report (as of December 2014), by Shinichi Mochizuki

Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki, by Ivan Fesenko

The slides for Yu. Hoshi's talk and photos of G. Yamashita's lectures at the RIMS workshop, March 2015  

Main texts:

[1]-[4] (currently being refereed) from p.4; plus the following papers are needed to various degree
[5], [6] from p. 1,
[16]-[17], [19] from p.2,
[21]-[23] from p.3
from the pdf file of papers of Shinichi Mochizuki

Files of the papers and useful comments to some of them are available from the page of Papers by Shinichi Mochizuki