A few quick links:
- There’s a one-day conference next Friday at the IHES, recognizing Dustin Clausen’s appointment to a new Jean-Pierre Bourguignon Chair. Should be several interesting talks, see here.
- There’s an ongoing conference at the KITP on the topic of What is String Theory? So far, none of the online talks address that issue. Evidently there was a discussion of the topic last Wednesday, but not recorded. Were any readers here in attendance and willing to report on that event? Next chance to find out what string theory is will be a Monday Blackboard Lunch talk by Gopakumar.
- In April there will be an IUT conference hosted by Zen University in Tokyo, see here. All the speakers but one are from RIMS. For news from the senior people devoted to IUT, Ivan Fesenko has moved to Westlake University in Hangzhou, and Shinichi Mochizuki is has been blogging here.
- There’s a new Shanghai Institute for Mathematics and Interdisciplinary Science, headed by Shing-Tung Yau.
- For those following what happens with the small number of permanent positions in particle theory, news from 4 gravitons.
Update: One more, which I’m quite interested in. Scholze will be giving a series of three Emmy Noether lectures at the IAS in March, topic Real local Langlands as geometric Langlands on the twistor-P1.
Peter : Gopakumar’s talk is online.
Shantanu,
I watched the talk. Basically his “What String Theory Is” answer is an explanation of the hope that large N QCD is a string theory (zero about string theory providing quantum gravity or unification). He takes this story up to about 25 years ago and AdS/CFT, doesn’t even mention the basic problem why this doesn’t give you QCD (no way to get asymptotic freedom). Asked what his fondest hope for 20 years from now, it was to find the string dual to QCD.
So, as for “What Is String Theory?”: string theory unification dead, only hope is to keep going on the AdS/CFT/QCD front and somehow make progress on an idea that thousands of people have been stuck on for 25 years.
Regarding the ABC conjecture, I believe that this paper that came out today by Kirti Joshi might be of interest: 2401.13508.
Related to IUT, although explicitly saying some steps are missing in Mochizuki’s papers, is the latest preprint by Joshi claiming to have now obtained a proof of several variants of Mochizuki’s Corollary 3.12 https://arxiv.org/abs/2401.13508
Kirti Joshi should do what Peter Scholze and Terence Tao did and get the Lean community to formally verify his papers on Mochizuki’s corollary 3.12 in the Lean proof assistant so that there are no doubts as to whether his proof is right or not.
Kurt Schmidt,
There’s no argument here that experts think works but needs more careful checking.
What’s needed in this case is just the standard procedure that the math community has developed over centuries to deal with a claimed proof: submit the paper to a first-rate journal for an impartial editor and referees to deal with in a manner acceptable to experts in the field.
The public fiasco of the IUT papers was caused by the failure to do this.
A common reaction I’m getting now when I ask experts about this is that too much time and attention has already been wasted on the topic, so not a good idea to give it more attention unless and until there are experts who have looked at it and think it works.
So, unless there’s news of that sort to report, enough of this for now.
It should be noted that in his latest paper Joshi claims to prove some lower bound on the size of certain sets Theta (so that something non trivial occurs in Cor 3.12), but not the Mochizuki type upper bounds that would lead to Diophantine applications (this was stated in the older paper https://arxiv.org/abs/2111.04890v1 “towards Diophantine estimates”, and the new paper appears to be an expanded version of that paper at the global level, it doesn’t provide a sharp upper bound, only in remark 7.8.3.2. that the upper bound is plausible in the global case).
somereader,
Thanks. I have been hearing comments about Joshi’s proof that it is unclear whether his version of the Corollary may differ from Mochizuki’s and not have the same implications, in particular not getting abc.
Peter: I know this is getting old. But, is it clear to anybody whether Joshi is claiming that this preprint is in fact supposed to truly prove abc itself (though the known steps following 3.12)? For a while I thought so, but interestingly I find that the string “abc” only appears twice in it, neither in a direct statement.
Doug McDonald,
One thing I have heard from some experts is that it is unclear to them whether Joshi is claiming a proof of abc.
To clarify the last comment, it’s pretty clear that Joshi is not explicitly claiming a proof of abc in this last paper. It would be great if someone would get him to state clearly whether or not this is supposed to be a proof of abc, and if not, what is missing.
One possibility that I can think of is that he hasn’t checked/doesn’t trust Mochizuki’s argument that 3.12 implies abc, and that he hasn’t come up with his own alternative argument using his own methods.
@Dr. Woit,
What you assert is indeed correct, I prefer to do my own due diligence independent of the claims of Mochizuki’s IUTT IV. The abc-conjecture is an expected, but delicate consequence of Corollary 3.12 (and some other results), but that is a work in progress and my conclusions (with proofs) will appear in my paper: Construction of Arithmetic Teichmuller Spaces IV.
In answer to your earlier post, my recently released paper (Constructions III) does provide many versions of Corollary 3.12 including Mochizuki’s version and I provide a `Rosetta Stone’ which facilitates a detailed comparison of the two theories. My formulation and proof of the geometric case of Corollary 3.12 is given in Constructions II(1/2) . For precise assertions, please refer to my papers.
somereader, Peter Woit
Kirti Joshi said that he will be proving the upper bounds in a forthcoming paper:
https://mathoverflow.net/questions/435110/consequences-of-kirti-joshis-new-preprint-about-p-adic-teichm%c3%bcller-theory-on-th/463562#463562