Dear Colleagues,
I am writing on behalf of the Organizing Committee of the two workshops
・“Invitation to Inter-universal Teichmüller Theory” (Notes)
・“Inter-universal Teichmüller Theory Summit 2021” (Notes)
held online at RIMS, Kyoto University, in September 2021. These two workshops are partof a yearlong RIMS Project“Expanding Horizons of Inter-universal Teichmüller Theory”
on topics related to Inter-universal Teichmüller Theory (IUT). Earlier this year, two otherclosely related anabelian workshops
・“Foundations and Perspectives of Anabelian Geometry” (Notes)
・“Combinatorial Anabelian Geometry and Related Topics” (Notes)
were also held online at RIMS.
I am writing, on behalf of the Organizing Committee of the two IUT workshops, to invite
you to register to view the Zoom videos from the two IUT workshops. Mathematicians
who attended the online Berkeley Colloquium talk “Classical Roots of Inter-universal
Teichmüller Theory” in November 2020 may think of these two IUT workshops as a sort ofvastly expanded version of this Berkeley Colloquium talk. Alternatively, mathematicians
who attended the online seminar・ “Promenade in Inter-universal Teichmüller Theory”
held at RIMS, Kyoto University, and Lille University (France) during the period September
2020 - April 2021 may think of these two IUT workshops as a sort of in-depth, concentrated
version of the RIMS-Lille seminar. Access to the Zoom videos from the two anabeliangeometry workshops mentioned above is also available for those who are interested.
Access to the videos will be provided to professional mathematicians (and graduate students
in mathematics) who register by sending an e-mail to any of the members of the Organizing
Committee stating the・name,・affiliation, and・Gmail address

of the person to be registered. Access will, at least initially, be provided until March 31, 2022
(the end of the Japanese school year), but may be extended further if there is sufficientinterest.
The videos may be shown to a few colleagues, but are not to be made public. Moreover, thevideos are to be used only for scholarly, mathematical purposes. In particular, the videos
are not to be used for non-mathematical purposes.
Many developments have come to pass in the nine years since the preprints on IUT werefirst made public in August 2012. The four original papers on IUT were published in theinternational mathematical journal PRIMS in March 2021. A subsequent paper by fiveauthors on explicit estimates in IUT, which gives a new proof of Fermat's Last Theorem, wasrecently accepted for publication in the Kodai Math. J. Moreover, three mathematicians
have begun writing a new series of papers on a generalized version of IUT withvarious new applications.
In particular, IUT continues to be a field of active
research and exciting new developments.
Unfortunately, it has come to my attention that certain misunderstandings concerning IUT
continue to persist in certain parts of the world. Perhaps the most famous
misunderstanding concerns an asserted identification of “redundant copies”. Thismisunderstanding involves well-known, essentially elementary mathematics at thebeginning graduate level concerning the general nonsense surrounding “gluings”. For
instance, if one “applies” this misunderstanding to the well-known gluing construction of
the projective line, then one concludes that the two copies of the affine line that appear in thisgluing are “redundant’’, hence may be identified. This identification leads immediately toa contradiction, i.e., to a “proof” that the projective line cannot exist! More details may befound in the Introduction to [EssLgc] and the references given there.
As discussed in [EssLgc], §1, such misunderstandings give rise to entirely unnecessary
confusion and can, at times, lead to deeply detrimental disruptions of the operational
normalcy of the field of mathematics (cf. [EssLgc], §1.10).
On the other hand, as discussed in [EssLgc], §1, the potent tools of(1) producing detailed, explicit, accessible, and mathematically substantive written
records of the mathematical reasoning underlying various assertions concerning IUT (cf.,e.g., article (6.) of the subsection entitled "Responsibilities of authors" ofthe EMSCOP (!); [EssLgc], §1.5) and(2) enhancing the mathematical and person-to-person interconnectivity (cf. [EssLgc], §1.11)oftheworldwide
mathematicalcommunity
byfostering constructive
mathematical dialogue (e.g., via e-mail and video meetings) among mathematicians
worldwide concerning issues of mutual interest

canplayanimportantunconstructive misunderstandings.

roleinovercoming

unnecessaryandIt is the sincere hope of the Organizing Committee that the workshop videos discussed above
can serve as a dynamic stimulus in promoting activities around the world of the sort
described above in (1) and (2) concerning IUT.

Sincerely,Shinichi Mochizuki ( motizuki@kurims.kyoto-u.ac.jp )On behalf of the Organizing Committee:
Benjamin Collas ( bcollas@kurims.kyoto-u.ac.jp )Ivan Fesenko ( ivan.b.fesenko@gmail.com )Yuichiro Hoshi ( yuichiro@kurims.kyoto-u.ac.jp )Shinichi Mochizuki ( motizuki@kurims.kyoto-u.ac.jp )Yuichiro Taguchi ( taguchi@math.titech.ac.jp )