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 2019-02-01: 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

(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 2019-02-01: 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