In March 2018, discussions concerning inter-universal Teichmuller theory
(IUTeich) were held at RIMS, Kyoto University. Participation in these
discussions was restricted to four mathematicians. This web page was
created, with the consent of the four participants in these March 2018
discussions, in order to make various files related to these discussions
available to the mathematical public. It is hoped that the material
posted on this web page will help to stimulate further constructive
mathematical discussions concerning this material. In this context, we
wish to emphasize that the material posted on the present web page is
by no means in final form and will be subject to further updates as
discussions progress.

The
fundamental misunderstandings concerning IUTeich documented in
these files --- as well as the situation (cf. [FskDsm], [FskPio]) surrounding
such misunderstandings that has arisen in the mathematical community ---
are most regrettable, not only for those directly involved in research and
dissemination activities concerning IUTeich, but also for the mathematical
community as a whole. On the other hand, at the time of writing, it appears
that the only way in which meaningful progress in remedying this situation
can be made is to further efforts to render the mathematical content that
is the subject of these misunderstandings
more explicit and more easily
accessible
, through further mathematical discussions and more detailed
manuscripts
. From this point of view, the files [SS2018-05], [SS2018-08]
are a significant first step, but are still relatively short and
do not contain
detailed, rigorous arguments
concerning numerous (often very strong)
assertions. Moreover, it does not necessarily appear realistic to expect that
further substantial efforts of the sort just described will be made by the
authors of these files [SS2018-05], [SS2018-08] in the immediate future.
In particular, further constructive mathematical involvement on the part of
mathematicians who did not participate in the March 2018 discussions has
the potential to yield substantial, meaningful progress in remedying this
situation.

Throughout the six years (2012-2018) since the release of the four preprints
on IUTeich, I, together with a number of colleagues, have addressed literally
hundreds (perhaps thousands) of technical questions from quite a number of
mathematicians concerning IUTeich via e-mail, skype, and in face-to-face
discussions. Many of these colleagues have written, or are in the process of
writing, detailed expositions of IUTeich. As is discussed in the final section of
[Rpt2018], the contents of the files posted on the present web page have been
discussed thoroughly with quite a number of these colleagues. Finally, we
recall that, during these six years, RIMS, Kyoto University, has contributed quite
substantial financial, administrative, and infrastractural resources to hosting
two large-scale workshops on IUTeich, as well as quite a number of visitors to
RIMS, for visits devoted (at least partially) to serious mathematical discussions
concerning IUTeich.

Any
professional mathematician (or graduate student) interested in engaging
in
serious, constructive mathematical discussions concerning this material
--- especially, any such mathematician who feels that he/she has a solid
mathematical understanding of the mathematical assertions made in the
files [SS2018-05], [SS2018-08], and, moreover, is interested in engaging
in constructive mathematical discussions concerning these assertions (where
we note that it is by no means clear, at the time of writing, that the set of
such mathematicians is nonempty!) --- is
encouraged to contact Shinichi
Mochizuki at the e-mail address given on the top page of this web site.




[Rpt2018] Report by Shinichi Mochizuki (with the cooperation of Yuichiro Hoshi)
 on the March 2018 discussions (updated on
2018-11-26: list of revisions)

[SS2018-05] May 2018 Report by the other participants in the March 2018
 discussions

[Cmt2018-05] Comments on [SS2018-05] by Shinichi Mochizuki

[SS2018-08] August 2018 Report by the other participants in the March 2018
 discussions

[Cmt2018-08] Comments on [SS2018-08] by Shinichi Mochizuki

[FskDsm] "About certain aspects of the study and dissemination of Shinichi
  Mochizuki's IUT theory" by Ivan Fesenko

[FskPio] "Remarks on aspects of modern pioneering mathematical research"
  by Ivan Fesenko

[FKvid] Video lecture (with English subtitles) on IUTeich by Fumiharu Kato

[YKId] Brief excerpt on the "id-version" of IUTeich from the lecture notes for
  a series of lectures on IUTeich given by Go Yamashita in November 2018
  at Keio University




March 2018 Discussions            on IUTeich