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: