Location: Room 420 Period: 2020-05-18〜2020-05-22

Organizers:

Ivan Fesenko (The University of Nottingham, UK)

Arata Minamide (The University of Nottingham, UK)

Fucheng Tan (RIMS, Kyoto
University)

Location: Room 420 Period: 2020-06-29〜2020-07-03

Organizers:

Yuichiro Hoshi (RIMS, Kyoto University)

Shinichi Mochizuki (RIMS, Kyoto University)

Ivan Fesenko (The University of Nottingham, UK)

Arata Minamide (The University of Nottingham, UK)

Inter-universal Teichmüller Theory Summit 2020

Location: Room 420 Period: 2020-09-08〜2020-09-11

Organizers:

Yuichiro Hoshi (RIMS, Kyoto University)

Shinichi Mochizuki (RIMS, Kyoto University)

Ivan Fesenko (The University of Nottingham, UK)

Yuichiro Taguchi (Tokyo Institute of Technology)

Location: Room 420 Period: 2020-09-08〜2020-09-11

Organizers:

Yuichiro Hoshi (RIMS, Kyoto University)

Shinichi Mochizuki (RIMS, Kyoto University)

Ivan Fesenko (The University of Nottingham, UK)

Yuichiro Taguchi (Tokyo Institute of Technology)

Location: Room 420 Period: 2020-09-01〜2020-09-04

Organizers:

Yuichiro Hoshi (RIMS, Kyoto University)

Shinichi Mochizuki (RIMS, Kyoto University)

Ivan Fesenko (The University of Nottingham, UK)

Yuichiro Taguchi (Tokyo Institute of Technology)

Chief organizer: Shinichi Mochizuki (RIMS, Kyoto University)

Organizing committee:

Yuichiro Hoshi (RIMS, Kyoto University)

Ivan Fesenko (Nottingham University, UK)

Yuichiro Taguchi (Tokyo Institute of Technology)

Fumiharu Kato (Tokyo Institute of Technology)

Masato Kurihara (Keio University)

Atsushi Shiho (University of Tokyo)

The
elucidation of the way in which the additive and multiplicative structure of
the integers are intertwined with one another is one of the most important and
central themes in number theory. In
August 2012, Shinichi Mochizuki (the proposer and chief organizer of the
present RIMS Research Project) released preprints of a series of papers
concerning **"Inter-universal Teichm****üller Theory"**, a
theory that constitutes an important advance with regard to elucidating this
intertwining. Moreover, the proof of the "ABC Conjecture", which follows as
a consequence of the theory, attracted worldwide attention. In the roughly
six and a half years since the release of these preprints:

・The number of**researchers who
have already acquired a thorough understanding of the theory**, as well as **advanced learners of the theory**, has
increased slowly, but steadily.

・Quite a number of**surveys and
related expositions** of the theory (7 of which have been made public, while
another 2 are currently in preparation) have been written, not only by the
author of the theory, but also by researchers who have already acquired a thorough
understanding of the theory.

・Although it is difficult to ascertain the precise number, at least on the order of 30**lectures** and **small-scale workshops** on the theory
have been conducted all over the world (in Japan, the UK, Russia, the US,
China, Germany, and France).

・At least 4**large-scale
workshops** (of one to two weeks in length) on the theory have been conducted not
only within Japan (in Kyoto, March 2015 and July 2016), but also in China
(in Beijing, July 2015) and the UK (in Oxford, December 2015).

As a result of these activities, a sort of**"inter-universal Teichm****üller theory community"**, consisting of between ten and twenty researchers, is currently in the
process of forming. Moreover, as a result of advances in research, such
as **combinatorial anabelian geometry**, based on ideas closely related to
the ideas that underlie inter-universal Teichmüller
theory, important links between research on inter-universal Teichmüller
theory and research concerning the **Grothendieck-Teichm****üller
group** and
the **absolute Galois group of the
rational numbers** have begun to form.

In light of these developments, the present RIMS Research Project seeks to bring together various researchers not only from the "inter-universal Teichmüller theory community", but also researchers interested in various forms of mathematics related to inter-universal Teichmüller theory, and to provide all such researchers an opportunity to engage in lively discussions concerning the various developments discussed above in an environment in which**interaction for
periods on the order of months** is possible, that is to say, unlike the
situation in the case of a single workshop (i.e., which typically only lasts
for roughly a week).

・The number of

・Quite a number of

・Although it is difficult to ascertain the precise number, at least on the order of 30

・At least 4

As a result of these activities, a sort of

In light of these developments, the present RIMS Research Project seeks to bring together various researchers not only from the "inter-universal Teichmüller theory community", but also researchers interested in various forms of mathematics related to inter-universal Teichmüller theory, and to provide all such researchers an opportunity to engage in lively discussions concerning the various developments discussed above in an environment in which