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I would like to know what was achieved in the workshop towards the verification of abc conjecture's proof and the advance of understanding of IUT in general.

A comment from a participant:

C Vincent (via Twitter) Omg, I think the speaker is actually proving ABC right now. There's an inequality that looks suspiciously like what we want. #IUTsummit

Inter-universal Teichmüller Theory Summit 2016 (RIMS workshop, July 18-27 2016) Organized by Fesenko, Mochizuki and Taguchi.

Myshkin
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tttbase
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    https://www.maths.nottingham.ac.uk/personal/ibf/files/dimitrov.pdf is slides from a presentation by Vesselin Dimitrov, Notes on the $\epsilon$ part in the $abc$ conjecture (Including Siegel zeros and effectivity in IUT). – Gerry Myerson Jul 29 '16 at 03:28
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    In Dimitrov's talk, what does "IUT implies no Siegel zero at negative discriminants" precisely mean? Maybe "IUT-III Cor. 3.12" as quoted at some other point? In the given situation, I don't know if I would consider "Result X in Mochizuki's work" to be a reasonable starting point for further investigation. It's sort of like the economist assuming there is a can opener. – post.as.a.guest Jul 29 '16 at 04:21
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    One could do worse than read all of Vincent's tweets. She at least gives some perspective of what occurred. – post.as.a.guest Jul 29 '16 at 04:23
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    What happens in the IUT summit at RIMS stays in the IUT summit at RIMS. – Asaf Karagila Jul 29 '16 at 06:04
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    As an aside, I am not entirely convinced (in Mochizuki's latest 115-page overview) of "alien copies" of structures corresponding by analogy to the traditional polar-coordinate evaluation of the Gaussian integral $I$ being equal to $\sqrt\pi$, as one gets $I^2=\pi$ therein, and an additional argument is needed to get the positive sign. Is this extra step available in the scheme-theoretic setting, with choices of units? The "justification of the naive approach" (1.7) makes it even more mysterious IMO, calling the answer $\sqrt\pi$ itself an error term! – post.as.a.guest Jul 29 '16 at 09:44
  • I have asked a more specific question with a less specific flag (soft question) but it was closed http://mathoverflow.net/questions/243750/recent-progress-on-the-verification-of-mochizukis-proof-of-the-abc-conjecture – Raphael J.F. Berger Jul 29 '16 at 15:10
  • Also they have recorded all talks on video, but they are not yet published, as far as I know. – Raphael J.F. Berger Jul 29 '16 at 15:18
  • If you do want to know what happened at the meeting then you should email a participant! – Stiofán Fordham Jul 29 '16 at 15:23
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    Here is a new Nature article from Castelvecchi which touches on the recent conference: http://www.nature.com/news/monumental-proof-to-torment-mathematicians-for-years-to-come-1.20342. – Raphael J.F. Berger Jul 29 '16 at 16:32
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    Also all slides of all talks from the conference are accessible from the conference website: https://www.maths.nottingham.ac.uk/personal/ibf/files/kyoto.iut.html some interesting comment by Ivan Fesenko is on his facebookpage (https://www.facebook.com/ivan.fesenko.37?fref=ts) and there are lots of comments on twitter mostly by Christelle Vincent and also by Taylor Dupuy (you might find them when you follow the link from OP). – Raphael J.F. Berger Jul 29 '16 at 21:20
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    Probably nothing. I don't understand the point of these vague questions. If you want to know something about Mochizuki work ask a more specific question (something about the slides or the papers) – user40276 Jul 30 '16 at 02:03
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    @post.as.a.guest: It means exactly what you say, that IUT-III Cor. 3.12 has the stated implication. Actually that proposition is not just a result in Mochizuki's work: it is the entire output of IUT theory, with everything after it being rather straightforward estimates that are not that hard do check. This is why I just said "IUT implies...," as everything really amounts to III 3.12. That being said, I share your feelings about this. My point was to try to clarify what precisely Mochizuki's inequality is, and what kinds of consequences might emerge if the methods get understood. – Vesselin Dimitrov Jul 31 '16 at 05:56
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    If you would like to ask a real question on Mochizuki's work (and not just one "designed to project sophistication", in the sense of Bill Thurston), then I think you need to be a lot more specific. Questions of the form "Has this-or-that work been verified?" are rather not suitable for MO, therefore I have voted to close as "unclear what you're asking". – Stefan Kohl Jul 31 '16 at 11:01
  • @StefanKohl +1 and thanks for that "project sophistication" line, regarding this question and some older ones concerning Grothendieck-ery. – Yemon Choi Jul 31 '16 at 18:54

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In my opinion this is a "non-question" in MO speak, but there has been an article and blogs about the "summit" by now, either of which may give you (or point to) more information. As indicated in the latter source, one should expect another round of such inquiries in early September (2016).

post.as.a.guest
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