The math department at Columbia this fall will be hosting three special lecture series, each with some connection to physics (at least in my mind…):

- Sergiu Klainerman will be lecturing on the proof of nonlinear stability for slowly rotating black holes, Wednesday afternoons at 2:45.
- Nikita Nekrasov’s lectures will be on The Count of Instantons, Friday afternoons at 1:30.
- The Eilenberg lectures will be given by Laurent Fargues on Some new geometric structures in the Langlands program, Tuesdays at 4:10.

Some other less inspirational topics:

- The news this summer from the LHC has not been good. On July 17 a tree fell on two high-voltage power lines, causing beams to dump, magnets to quench, and damage (a helium leak) to occur in the cryogenics for an inner triplet magnet. See here for more details. Fixing this required warming up a sector of the ring, with the later cooldown a slow process. According to this status report today at the EPS-HEP2023 conference in Hamburg, there will be an ion run in October, but the proton run is now over for the year, with integrated luminosity only 31.4 inverse fb (target for the year was 75).
- The Mochizuki/IUT/abc saga continues, with Mochizuki today putting out a Brief Report on the Current Situation Surrounding Inter-universal Teichmuller Theory (IUT). The main point of the new document seems to be to accuse those who have criticized his claimed proof of abc of being in “very serious violation” of the Code of Practice of the European Mathematical Society. This is based upon a bizarre application of the language

Mathematicians should not make public claims of potential new theorems or the resolution of particular mathematical problems unless they are able to provide full details in a timely manner.

to the claim by Scholze and Stix that there is no valid proof of the crucial Corollary 3.12. It would seem to me that Mochizuki is the one in danger of being in violation of this language (he has not produced a convincing proof of this corollary), not Scholze or Stix. The burden of proof is on the person claiming a new theorem, not on experts pointing to a place where the claimed proof is unsatisfactory. Scholze in particular has provided detailed arguments here, here and here. Mochizuki has responded with a 156 page document which basically argues that Scholze doesn’t understand a simple issue of elementary logic.

Also released by Mochizuki today are copies of emails (here and here) he sent last year to Jakob Stix demanding that he publicly withdraw the Scholze-Stix manuscript explaining the problem with Mochizuki’s proof. Reading through these emails, it’s not surprising that they got no response. The mathematical content includes a long section explaining to Scholze and Stix that the argument they don’t accept is just like the standard construction of the projective line by gluing two copies of the affine line. On the topic of why he has not been able to convince experts of the proof of Corollary 3.12, Mochizuki claims that he convinced Emmanuel Lepage and that

one (very) senior, high-ranking member of the European mathematical community has asserted categorically (in a personal oral communication) that neither he nor his colleagues take such assertions (of a mathematical gap in IUT) seriously!

I suppose this might be Ivan Fesenko, but who knows.

- Since the Covid pandemic started, the World Science Festival has not been running its usual big annual event here in New York. This fall they will have an in-person event, consisting of four days of discussions moderated by Brian Greene. In particular there will be a panel Unifying Nature’s Laws: The State of String Theory evaluating the state of string theory, featuring four of the most vigorous proponents of the theory (Gross, Strominger, Vafa and Witten). I suspect their evaluation may be rather different than that of the majority of the theoretical physics community.

**Update**: Quanta has a very good article by Kevin Hartnett about the telescope conjecture in homotopy theory and its recent disproof. This is due to work of Ishan Levy, Robert Burklund, Jeremy Hahn and Tomer Schlank, all of whom gave talks on the subject at the Oxford conference this past June in honor of the 65th birthday of Mike Hopkins. Videos of the talks are available here. If homotopy theory is not your thing, and if you haven’t heard Graeme Segal speak recently about his thinking on the definition of quantum field theory, you could instead watch his talk.

**
Update**: Video of Klainerman’s lectures will be available here:

David Gross was born in 1941, Edward Witten in 1951, Andrew Strominger in 1955, and Cumrun Vafa in 1960. Why did they decide to select 3 Boomers and 1 member of the Silent Generation to host the string theory panel, rather than a younger string theorist who could speak for the younger generations?

Kurt Schmidt,

With Witten in the lead, all four of them jumped on the string theory unification bandwagon at the beginning in 1984-85. Since then and to the current date, they have been among the most prominent proponents of the subject. So, if you want to know what the hard-core, true believers who have been at it for nearly forty years think, this is the right panel. If you wanted a sober evaluation of where we are after those forty years, you’d choose a different panel.

I don’t wish to pile on the ageism, but the idea of “string unification” seems to have become rather quaint these days, hasn’t it? What would such a panel have to say that would be of much relevance to even string theory’s most ardent supporters at present? It’s been many years now that all the press seems to be about using string-adjacent techniques to make toy models of black holes, wormholes, condensed matter and so forth. Witten himself explicitly capitulated on anthropism, so what more is there to discuss about the parochial details of our pocket of the multiverse?

LMMI,

Of the five (including Greene), Vafa is the only one still trying to make an argument that string theory has some implications for the real world (his “swampland program”). All the others have completely given up on this, but continue to try to sell this failure as some sort of success. Andy Strominger takes this the furthest, see for instance here

https://www.math.columbia.edu/~woit/wordpress/?p=11138

dealing with the failure of 1980s hype by claiming that string unification would have been boring small potatoes:

“I think that the idea that people were excited about back in 1985 was really a small thing, you know, to kind of complete that table that you put down in the beginning of the spectrum of particles…”

Now he’s replacing that with new, improved hype about space-time. It seems to me that what he learned from the past was that hype works, best to just keep at it.

Perhaps if Mochizuki can convince Lepage to publicly state he thinks the IUT papers are all correct, and

whythe proof of Corollary 3.12 in IUT3 is solid, then Mochizuki might have a tiny bit more support. At present, it seems like hearsay. Also, all this vague references to senior experts etc without saying who they are is of rather little worth without them being public in their support.David Roberts,

Mochizuki gives a list of those who he says have worked on understanding the Scholze/Stix criticism of the proof:

“”Yuichiro Hoshi, Go Yamashita, Arata Minamide, Akio Tamagawa, Ivan Fesenko, Mohamed Saidi, Emmanuel Lepage, Benjamin Collas.”

The damning fact is that to this day none of those people has written or lectured on their supposed understanding of how the proof overcomes the Scholze/Stix objections.

As for his claim about a “(very) senior, high-ranking member of the European mathematical community”, Mochizuki completely blows up the credibility of this claim by saying that none of this person’s colleagues take Scholze/Stix seriously. He repeatedly has gone on like this, claiming that no one he talks to takes the objections to the proof seriously, or knows anyone who does, which indicates that he has isolated himself to a disturbing extent.

Prof. Klainerman used all his might

to deduce a new theorem last night.

It’s a breakthrough for sure,

but the proof is obscure

and takes two thousand pages to write.

Is there a video of the talk by Klainerman somewhere? I’m quite interested in watching that. Thanks!

Alex,

I don’t know if there will be video of one or more of these three lecture series this fall. If there is, I’ll add a link here, also likely available at Columbia math dept. youtube channel.

I was under the impression that Scholze and Stix did not publish their report, but gave it to Mochizuki privately, for him to do with it as he wished. Mochizuki then chose to post it on his own website. Do I have the facts right? If so, then it would seem strange for Mochizuki to request that Scholze and Stix “publicly withdraw” their “manuscript” when Scholze and Stix were not the ones to publicly release the report in the first place.

I can’t make it for the Laurent Fargues presentation on the 12th, anybody know if it will be available online after? Thanks

Will the Nekrasov lectures be made public?

Peter,

Yes. First should appear on dept website next week.