- The Stacks Project (see an earlier post here) had a very successful workshop in Ann Arbor earlier this month. This is a remarkable effort pioneered by Johan de Jong to produce a high quality open source reference for the field of algebraic geometry. It now is over 6000 pages, with an increasingly large number of papers citing it (according to data from Pieter Belmans, 85 citations in the arXiv so far in 2017 alone). During the workshop plans were discussed for the future of the project, with work on a new version of the project infrastructure underway (see slides and a blog post from Belmans).
- The latest AMS Notices has a wonderful article by my Barnard/Columbia colleague Dusa McDuff about her remarkable family history and reflecting on her equally remarkable mathematical career. A post earlier this year discussed a Quanta article about her recent work with Katrin Wehrheim on technical issues in the foundations of symplectic topology. Kenji Fukaya has recently written something for the Simons Center website (see here) explaining his take on this story.
- The Stanford Encyclopedia of Philosophy has a new entry about the fine-tuning problem, by Simon Friedrich.
- The LHC operators have run into some difficulty in recent weeks (reflected in the accumulated luminosity plots here and here), with problems centered around an unknown source of gas in the beam pipe at a specific location, leading to losses of the beam. Some information about this is available here. The past few days they seem to be having success running the machine with around 1500 bunches, much less than the 2500 or so of earlier in the summer. The target for the year is 40 inverse fb which may still be achieved, while more optimistic numbers that looked plausible earlier now seem less likely.

**Update**: Joe Polchinski has put on the arXiv a long autobiographical document, with a detailed discussion of his scientific career.

**Update**: As mentioned in the comments, Go Yamashita has posted a long document surveying Mochizuki’s claimed proof of the abc conjecture. Experts may find that this makes it more possible to understand and check the claimed proof, we’ll see.

**Update**: Also at the Simons Center website, there’s an interview with Michael Green. It’s interesting to see that in recent years his research interests have led him to getting closer to mathematics and to an appreciation of what mathematicians do. As for his claim about string theory that

I donâ€™t think there is a substantial antagonism to it among those who have studied it, other than a few individuals who enjoy publicizing their views.

I think he’s quite wrong if you properly take “it” to refer to the aspect of string theory there is widespread antagonism to among physicists, the overhyped claims about a unified theory based on string theory.

Peter any comments about Nima’s talk at TevPA?

The SEOP entry on Fine Tuning was very interesting and helpful. Thank you for posting the link.

I second neil’s thanks.

Peter,

Polchinski writes about himself: “The three times that I shook up the field – D-branes, the string multiverse, and firewalls – might give you the impression that I am a radical, but it is not by design.” I never met him, but are these three achievements really his main legacy?

Polchinski also writes in the text that he got “brane cancer”. What an unfortunate lapsus. Somebody should let him know.

I didn’t see any reference to this: the not-so-fine-tuned universe:

http://cosmos.nautil.us/feature/113/the-not-so-fine-tuning-of-the-universe

Apropos a previous blogpost on this website, the survey of Yamashita on work of S. Mochizuki has appeared http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc_ver6.pdf 294 pages and claims to be self-contained.

Klaus,

My guess is that “brane cancer” is intended as humor on Polchinski’s part. I wish him well and he’s entitled to some levity about the difficult situation he is in.

Yes, I think it’s right that those are the three things he has done that have gotten the most attention and had the most impact. Unfortunately for one of them (moduli stabilization/string theory landscape/multiverse) I think the impact has been large and negative and, away from the West Coast, I suspect many of his colleagues agree with me. His discussion in his memoir of how this work affected him is remarkable.

BTW, (maybe you have already known this:-) ) Weinberg is going to give a talk to celebrate 50 years of SM https://indico.cern.ch/event/649760/timetable/ . Kind of curious about what he is going to say in the talk

I found Section A.4 on pages 265-266 of Yamashita’s manuscript quite fascinating.

Philosopher here. I’m curious how many mathematicians, if any, suspect that Mochizuki is perpetuating a hoax. I am thinking of all the new names M. gives to concepts that are already perfectly well denoted (e.g. isomorphism); all the jargon, generally; the way a proof in one paper relies on a result from a second, which uses a definition from a third, which relies on a lemma from the first one–i.e. all the circularity; the apparent unwillingness on M.’s part to make the argument perspicuous for others; and the fact that experts are unable to understand the basic strategy of the proof. None of these features is dispositive of a hoax, but they are worrying.

Do mathematicians think that? Or is the general sentiment that M.’s work really is too brilliant and cutting-edge to understand? Or is M. likely mistaken, but working in good faith? Are mathematicians really just at a loss about what to think?

Tom,

I don’t know of any mathematicians who think it’s a hoax, there’s nothing at all to indicate that. All indications are that it’s a complex argument, based upon ideas involving a lot of new mathematical constructions. The question is whether these new constructions do what Mochizuki argues that they do. Surely he is convinced of this, but others need to understand the new constructions well enough to see whether the arguments are airtight. This is a very unusual situation: usually by now other experts would have assimilated the new ideas well enough to check them, or to identify their weaknesses. Perhaps the Yamashita survey will help move this along. I think it’s fair to characterize the current situation as “at a loss about what to think”.

S. Mochizuki has a good pedigree and has done first-rate mathematics in the past. Furthermore there are other first-rate mathematicians who believe he is on to something. So it is rather hard to completely ignore his work, despite his unwillingness to engage properly with the community.

Quanta Mag has a popular-science article on efforts of getting QM from a few axioms:

Quantum Theory Rebuilt From Simple Physical Principles

I remember Lucien Hardy’s

Quantum Theory From Five Reasonable Axioms, and that dates back to even before the Forever War.

Axioms are not “physical principles” but “syntactic principles” though. You can just feed them to a TM-based deduction system (or better) w/o physics in sight.

QM rebuilds seem to be not particularly hard, what about QFT rebuilds?

Spaghetti-code mathematics is, unfortunately, quite common at the highest levels. It can easily take a decade or two or three before important work gets understood, an intelligent organization is found, the proofs are actually verified, and so on. The recent Quanta article on McDuff’s attempts to make sense of the foundations of symplectic geometry could have been rewritten by changing the names and theorems around.

No need to invoke

abcparanoia.Regarding Yamashita’s survey: I doubt it does very much to improve understanding of Mochizuki’s work. Especially in the latter part of the survey proofs of theorems consist only of “follows from the definitions”, while the theorem statements can be several pages long!

Peter,

As far as you know, are there plans for the LHC to be upgraded in luminosity and/or energy before it shuts down completely? If so, is there already a timeline established for when these will arise and factors of increase for either luminosity and/or energy?

Andrew,

There are plans to upgrade the luminosity of the LHC significantly (the “HL-LHC”) and the energy slightly (from 6.5 to 7 TeV/beam), these plans go out to 2035 of so, see here:

http://lhc-commissioning.web.cern.ch/lhc-commissioning/schedule/LHC-schedule-update.pdf

I don’t know of any further ideas about higher luminosity. There are post-HL-LHC plans (“HE-LHC”) for a possible doubling of the energy of the beams. This would require developing new magnets and replacing much of the current LHC with them. Unclear how likely that is to happen. It would be expensive, but much less than other proposals which would require building a new, larger tunnel.

Why doesn’t someone set up a wiki and have a group of mathematicians go through the Mochizuki/Yamashita presentation and confirm the theorems one by one. When they get to one they don’t agree with or understand, just say “unverified”. I understand this is a long proof, but where is the consensus on what’s wrong exactly? I can’t believe it’s taking this long to get a clear answer.

asdfasdfff,

Unfortunately the problem seems to be that Mochizuki’s proof is written up in a form spread over many papers, very hard for anyone to go through and check step by step. One point of view on the current situation is that it is his responsibility to rewrite the proof in a form such that experts can do this. The Yamashita survey is supposed to provide a roadmap to the Mochizuki papers, outlining the logic of the proof. It is only recently available, presumably some people are trying to go through it as you suggest.

My impression from what I hear is that some of the experts who have tried to understand the proof have gotten stuck at more or less the same point. Perhaps the Yamashita survey clarifies that point, maybe not. A significant part of the problem here is a breakdown in the usual way such a situation normally gets resolved: communication between experts and the author of the proof, providing explanations satisfactory to the experts. Achieving this was a goal of a couple workshops, but these did not reach this goal, and I don’t know what the current situation is for more attempts.

The Yamashita paper has done at least one very useful thing: it’s collected the proof that one only needs to consider a very special case to prove the whole Szpiro conjecture (which implies abc). This proof (due to Mochizuki) was until now spread over several of his papers, and in Yamashita’s write-up uses standard-looking arithmetic/anabelian geometry. Moreover, Yamashita provides a statement (beyond the inequality the Szpiro conjecture reduces to) that uses quite standard terminology that the IUTT papers are aiming to prove. It’s small progress like this that will chip away at the monolith that is IUTT, which unfortunately is very smooth and hard.