Yet More About Grothendieck

Since Grothendieck’s death somewhat more than a year ago, quite a lot of new material about him and his mathematics has become available. Visit the Grothendieck Circle to find a lot of this, with just one example some new chapters of the English translation of the third volume of Scharlau’s biography.

This month’s AMS Notices has the first of two parts of a long article with contributions from many mathematicians discussing Grothendieck’s work and their memories of him and his influence on their careers. Colin McLarty has an excellent expository article, maybe the best of attempts I’ve seen to explain some of the themes of Grothendieck’s mathematics in a relatively accessible manner.

While you’re there, this latest issue of the Notices has quite a bit else worth reading, from my colleague Ivan Corwin on KPZ universality to Beilinson on Gelfand’s seminar, and an amusing attempt by Jeremy Gray to guess not the next Fields medalist, but who would have gotten one in 1866.

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This Week’s Hype

This week’s dramatic announcement of the discovery of gravitational waves was a major milestone for the fields of physics and astrophysics. The LIGO observation validates a lot of previously untested aspects of our understanding of general relativity, and promises the imminent opening up of a new field of observational astronomy, as LIGO sees other astrophysical sources of gravitational waves. Watching the announcement, the lead up to it, and the press stories that came out, many immediately as the embargo was lifted, I was struck by the general high quality of the stories in the press (I linked to a few of them in the last posting, but there are many more). Congratulations to whoever organized this, and to all the science writers who have done a great job producing enthusiastic but generally hype-free coverage of the story.

Unfortunately, those physicists brought in by major news organizations to tell the public what the significance of this is often can’t resist the temptation to indulge in the usual hype. At the Wall Street Journal today, Michio Kaku’s commentary is labeled Riding Gravity Waves to the Big Bang and Beyond, and subtitled “Once again, Einstein’s theory of relativity is confirmed by scientists. Next stop: Creation.”

There’s nothing in his piece about what else LIGO might observe and what we might learn from it about the universe. Instead, it’s all about the big bang, Creation, and before the big bang, things which as far as I can tell, LIGO data is highly unlikely to tell us anything about:

Now we are witnessing the third great revolution in telescopes, the use of gravity waves to open a new chapter in astronomy. For the first time, waves from the very instant of creation might be observed, giving us “baby pictures” of the universe as it was born. High-school textbooks may have to be rewritten to incorporate the new discoveries coming from this third generation of telescopes.

This may also have philosophical implications. Right now the big-bang theory doesn’t tell us what banged, why it banged, and what caused it to bang. It only tells us that there was a bang. But if space-based gravity-wave detectors similar to LIGO’s detectors can measure the radiation emitted an instant after the big bang, then, using mathematics, one can run the equations backward to determine what set off the big bang in the first place, in effect answering the biggest question of all: What banged and why?

When Einstein postulated gravity waves a century ago, he not only opened up an entirely new chapter in astronomy, he also opened the door to answering the most important philosophical questions of all time, including the creation of the universe.

Over at the New York Times, in the Sunday Review, Lawrence Krauss has a more sensible piece, entitled Finding Beauty in the Darkness. Multiverse mania seems though to be irresistible, as he ends up with this summary of the physics significance:

Ultimately, by exploring processes near the event horizon, or by observing gravitational waves from the early universe, we may learn more about the beginning of the universe itself, or even the possible existence of other universes.

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Gravitational Wave Predictions

I think I can confidently predict that tomorrow morning either one of two things will happen:

  • The first observation of gravitational waves will be reported by the LIGO experiment.
  • A large fraction of the scientific community will be really, really angry at members of the LIGO collaboration.

I’m betting on the first of these two alternatives, and like everyone else will be watching to see what happens tomorrow. If you want some informed commentary on what it all means though, this isn’t the place (what I know about gravitational radiation is basically the little that I learned in a GR course about 40 years ago…), so for now I’ll leave comments closed.

One place advertising a live feed is Nature. I’ll be happy to list better possibilities here if people let me know about them.

Update: Another place to try for the webcast is here.

Update: Big event here at Columbia. Roone Arledge auditorium packed.

Update: Quite amazing, just as predicted, observation of two black holes coalescing, a historic discovery. That stuff I was taught 40 years ago really works. More details many places as the embargo is lifted, with some good examples Natalie Wolchover at Quanta, Dennis Overbye at the New York Times, and Davide Castelvecchi and Alexandra Witze at Nature. The paper has been refereed and is here at PRL.

Update
: Better info about the waves is available elsewhere, but I can report here on something pretty amazing: my graduate school roommate’s gravitational wave soup bowl.

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Stacks Project Party

Last night I got to attend a major event of the Manhattan social season, a party celebrating the fact that the Stacks Project has reached the milestone of 5000 pages. As far as anyone knows, no one has ever printed out the whole thing, but to give an idea of scale, the party featured a large stack of reams of paper totaling about 5000 pages.

I was going to include a party report, describing the various celebrities there, their outfits and conversations, but one of them (Mathematics Without Apologies) has its own blog, so I’ll just refer you there.

For some background about this amazing project, from when it was a mere 4000 pages, see here.

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Rutgers Talk

Slides from my talk at Rutgers are now available here. The idea was just to advertise to physicists there the point of view that is all too familiar to regular readers here. The final speculative comments about relations to mathematics shouldn’t be taken too seriously, these are things I hope to work on and write about much more in a few months once my current book project is completed.

Update: Interestingly, my Princeton advisor Curt Callan yesterday gave a talk at the KITP with a bit of a similar theme, starting off by arguing that the success of the standard model made future progress in HEP very difficult. His answer to the problem is quite different than mine (his involves trying to make contributions to biology). The first question at the end (from David Gross) is about the relation to new mathematics.

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Some News

Not much time for blogging at the moment, with one reason that I’ll be giving a talk at Rutgers on Wednesday, and need to get that prepared. A few quick items:

  • As some commenters have mentioned here, talks from the recent Munich conference (discussed here) are now available. From the little time I’ve found to look at them, I think Rovelli’s is the talk that makes the point about all of this most worth making, with Massimo Pigliucci good at explaining the wider implications.
    While interesting comments on the talks are encouraged, for reasons that I can’t explain publicly, discussion here of the Polchinski contribution is not welcome.
  • Besides watching Gordon Kane in Munich on string theory predictions, he also has a paper about this out now.
  • Congratulations to Bert Kostant on the award of the 2016 Wigner Medal. Kostant has been one of the major figures over the years in developing many deep ideas about the intersection of mathematics and physics, as well as a leading figure in the algebraic approach to Lie algebras and their representations.
  • A lot of mathematicians and physicists want you to use TurboTax.
  • Steven Weinberg’s sensible opposition to guns in UT Austin classrooms has gotten a lot of media attention (for instance here). Of the many obvious reasons why this is a bad idea, he correctly points out that it may well make it difficult for UT to recruit faculty.

Update: A commenter points out that more videos from the Munich conference are available here.

Update: John Horgan has a wonderful interview with the remarkable and ubiquitous Sabine Hossenfelder. Highly recommended.

Update: For news from the LHC, see last week’s Chamonix LHC performance Workshop. From the summary, the goal is about 30 inverse fb of pp collisions this year.

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More From Polchinski

Joe Polchinski has a rather odd preprint on hep-th, more of a blog posting than a paper, summing up his views on string theory and the multiverse. This is a revised version, wisely dropping a really unfortunate section. The material previously here explaining the background to what was in that section has been moved, and I’ve renamed the posting.

I’ve never personally met Polchinski, and from those who know him I’ve heard that he’s a nice guy. I’ve also recently heard that he’s ill, wish him the best.

Update: It seems that I misunderstood why Polchinski removed the section about me from his arXiv article. He’s now claiming that it was just because, since he’d gotten trackbacks to my blog banned, it would be unfair that there would be no trackback to his article (true enough…). This whole situation is a level of bizarre beyond the heights reached way back when during the string wars.

For those reading the version of Polchinski’s article on his website rather than the current one on the arXiv, to understand what this is about, please read the material here.

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Hitler doesn’t get a postdoc in High Energy Theory

I recognize that this is a genre that is a bit tired, and arguably in poor taste, but the commentary on the HEP theory postdoc job market in the video Hitler doesn’t get a postdoc in High Energy Theory is insightful. As far as I can tell the HEP Theory postdoc/junior faculty market has been the same for the last 45 years or so: far more people than jobs, and if you want one you better be working on one of a small number of “hot” topics. One might speculate that this correlates with the lack of progress in the field during this time. I’m a bit better informed about the mathematics job market for fresh PhDs, which is much healthier, as is the intellectual state of the field.

A recent trend does seem to be fewer jobs in the US, more in Europe. Anyone with better information about what is going on is encouraged to comment here (and, condolences if this is because you’re on the market).

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Back at Work

It’s been a while since the last posting here, mostly because I’ve been away on vacation, but also because I haven’t seen anything that newsworthy. But, since I’m back in the office and there have been complaints, here are a few items:

  • For the first time in a very large number of years, a new volume has appeared in the series of Bourbaki treatises, dealing with algebraic topology (table of contents here). From the table of contents, it appears to be a rather modern treatment mostly of the fundamental group, but still in the Bourbaki style of exhaustive coverage and abstract point of view (I don’t see any mention there of actually computing the fundamental group of anything…).
  • While in Paris I attended some of the Seminaire Bourbaki talks. You too can watch via Youtube, or read the written versions.
  • Far from mathematics and physics, one thing I did in Paris was stop by a store selling Breton products, and had a discussion with the owner about Kouign Amanns. He had a short hand-written list of a few places they could be had in the US. When I got back here, the next morning I went out to my local bakery (Silver Moon, at Broadway and 105th), and found that while I was away they had started selling them.
  • On the Mochizuki front, there’s a new paper by Vesselin Dimitrov, claiming that if Mochizuki’s argument is correct, it implies something even stronger than Mochizuki claims, an effective version of the abc conjecture. The next workshop about this will be in Kyoto in July. One mathematician who has gotten interested in this and is listed as planning to attend is Edward Frenkel.
  • If you can’t get enough of the “Is HEP physics dead or what?” debate, see John Horgan on How Physics Lost its Fizz.
  • Among the things going on here at Columbia this semester, there are Eilenberg Lectures on geometric representation theory (starting in a few minutes…) by Roman Bezrukavnikov, a course by Michael Harris on Lafforgue’s recent work on the Langlands correspondence for function fields (also the topic of one of the Seminaire Bourbaki talks), and a conference celebrating Dusa McDuff’s 70th birthday.

Better leave now to get a seat at the talk…

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Various and Sundry

Some short items on a wide variety of topics:

  • The Hawking/Perry/Strominger paper on a new idea about the black hole information paradox (see here for an early discussion) based on BMS supertranslation symmetries has now appeared on the arXiv. I’m no expert on the intricate arguments about this paradox, so have no idea what the implications of this paper for that really are. However, it does seem to be a very interesting approach to quantum gravity questions (although the paper mostly deals with simpler gauge theory calculations). The ideas are squarely in the mainstream of what has been the most successful way of making progress in fundamental theory: identifying new implications of symmetries that are at the center of our core theories (the standard model and GR). Such a new understanding looks like a far more promising way forward than much of what is currently popular in the subject.
  • For an example of what is currently popular, the KITP is hosting a workshop this week of the the It from Qubit Simons Collaboration, on Quantum Error Correction and Tensor Networks. I gather this is supposed to somehow explain AdS/CFT, but I’ve never understood how this is supposed to come about. Evidently I’m not the only one wondering about this. John Presskill reports that, in his talk leading off a series of lectures on this, Patrick Hayden commented that

    I’m unsure what we are trying to learn from these tensor network models of holography.

  • Tonight PBS will be showing the film Particle Fever, which I wrote about here. It’s a great film, highly recommended, despite the larding with comical nonsense about the multiverse (if you believe the theorists in the film, the multiverse is supposed to be tested by its prediction of a mass of 140 GeV for the Higgs). The capsule summary in the New York Times TV listing this morning for the film is “Scientists recreate conditions from the big-bang theory”. While the LHC has nothing to do with the big-bang theory, maybe this summary refers to the comedy of the theorists and another well-known TV show, in which case viewers may be a bit disappointed.
  • In other LHC related news, the AMVA4NewPhysics project now has a blog, latest posting explains the basics of b-tagging.
  • I’ve never been able to really make sense of many of the arguments about “Bayes’s Theorem”, and the recent attempts to justify string theory using this just seemed bizarre. John Horgan has a great explanation of what is going on here, including this take on the Bayes/string theory/multiverse business:

    In many cases, estimating the prior is just guesswork, allowing subjective factors to creep into your calculations. You might be guessing the probability of something that–unlike cancer—does not even exist, such as strings, multiverses, inflation or God. You might then cite dubious evidence to support your dubious belief. In this way, Bayes’ theorem can promote pseudoscience and superstition as well as reason.

    Embedded in Bayes’ theorem is a moral message: If you aren’t scrupulous in seeking alternative explanations for your evidence, the evidence will just confirm what you already believe. Scientists often fail to heed this dictum, which helps explains why so many scientific claims turn out to be erroneous. Bayesians claim that their methods can help scientists overcome confirmation bias and produce more reliable results, but I have my doubts.

    And as I mentioned above, some string and multiverse enthusiasts are embracing Bayesian analysis. Why? Because the enthusiasts are tired of hearing that string and multiverse theories are unfalsifiable and hence unscientific, and Bayes’ theorem allows them to present the theories in a more favorable light. In this case, Bayes’ theorem, far from counteracting confirmation bias, enables it.

  • The recent Munich conference trying to justify string theory by Bayesian methods wasn’t the only example of European funding for philosophers to weigh in on the latest in fundamental physics. Another just announced European LHC-related project is a 2.5 million Euro research unit aiming to investigate the LHC “from an integrated philosophical, historical and sociological perspective.”
  • I just ran across a recent paper by Kristian Camilleri and Sophie Ritson on The role of heuristic appraisal in conflicting assessments of string theory. It is very good, unlike almost every other discussion of this topic, I think it gets right the central serious argument of the “string wars”: how does one evaluate the prospects for the string unification idea? There is no simple answer to this, you need to understand what the state of efforts to connect a hoped for unified string theory to reality really are, how they have evolved, and try to make a sensible judgment about whether this is a failed idea or whether there is hope left. I highly recommend reading this for those who are not completely tired of this subject.
  • In the same journal I noticed another quite good article, by Porter Williams on naturalness. He carefully explains the different incarnations of “naturalness” and I think comes to the right conclusion that it is best thought of as the idea that physical behavior at widely different distance scales should not be correlated. By the way, the name “naturalness” for this is a bit of marketing genius (how could “nature” not be “natural”?).
  • In geometric representation theory news, the Simons Center is running a program on the topic this month, videos here. Here at Columbia Roman Bezrukavnikov will be the Spring 2016 Eilenberg lecturer, with his topic “Geometric categorification in representation theory”. I believe talks will be Thursdays at 2:40, watch the Columbia math department website for more news.
  • Personally, I’m about to head out tomorrow night on vacation, so expect minimal blogging and possibly even shutting off of comments. When I get back, I’ll be teaching our spring semester graduate course on groups and representations, see here. Also trying to finish my book on quantum theory and representation theory. Current state (see here, comments always welcome) is that I’ve gone over and rewritten the first 34 chapters (except the introduction), planning on rewriting and adding material to the rest of the manuscript this semester. This better be done by this summer, partly because that’s when it is supposed to be delivered to Springer, partly because I’m already quite tired of this project and want to work on other things…

Update: Any mention of Bayesianism seems to attract a large number of people who want to discuss it, especially aspects that have nothing to do with the string theory/multiverse business. Please discuss this topic with John Horgan at his blog.

Update: Sabine Hossenfelder has more on the Hawking/Perry/Strominger paper here.

Update: Scientific American has an interesting interview with Strominger, who explains some of the ideas behind Hawking/Perry/Strominger. Jacques Distler has come out of retirement at Musings to object that this work violates two central ideological tenets: one should not pay attention to gauge invariance, and the answer to all questions should be string theory or AdS/CFT.

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