Langlands/Frenkel and Some Other Things

Posted on November 16, 2018 by woit

The Canadian publication The Walrus today has a wonderful article about Robert Langlands, focusing on his attitude towards the geometric Langlands program and its talented proponent Edward Frenkel. I watched Frenkel’s talk at the ongoing Minnesota conference via streaming video (hopefully the video will be posted soon), and it was an amazing performance on multiple levels. A large part of it was a beautiful explanation of the history and basic conception of what has come to be known as geometric Langlands. He then went on to explain carefully some of the ideas in the recent Russian paper by Langlands, basically saying that they worked in the Abelian case, but could not work in the non-Abelian case. He ended by describing some alternate ideas that he is working on with David Kazhdan. Langlands was in the audience and at the end of the talk rose to comment extensively, but I couldn’t hear his side of this since he had no microphone (that Frenkel was sticking to his guns though was clear).

Besides giving the talk, Frenkel has made available a manuscript which gives a much more detailed version of the talk. See section 3.5 for an explanation of what he sees as the fundamental problem with what Langlands is trying to do: even in the simpler case of G/B over the complex field, you can’t successfully define a Hecke algebra in the way that Langlands wants.

The conference is finishing up right now, with final remarks by Langlands coming up later this afternoon.

A few more items, mostly involving my Columbia math department colleagues:

  • If you connect quickly to the streaming video from Minnesota, you may be able to catch Michael Harris’s talk on local Langlands.
  • Quanta magazine has an article about a recent proof of an old conjecture by Dorian Goldfeld about ranks of elliptic curves. This is due to Alexander Smith, now a third fourth year graduate student at Harvard (he started working on this while an undergrad at Princeton, with Shouwu Zhang). His twin brother Geoffrey is also a math grad student at Harvard.
  • Andrei Okounkov has been giving some talks recently at various places about developments in geometric representation theory with some connection to physics, under the title New worlds for Lie Theory. The slides from the ICM version of the talk are here.
  • For those more interested in physics than mathematics the new issue of Inference has some articles you might enjoy. In particular, Sheldon Glashow is no fan (neither is Chris Fuchs) of the book I reviewed here

Update: Michael Harris is appearing via Skype from his home near here, since transportation out of NYC yesterday was mostly shut down (very early season unprecedented snowstorm, during rush hour…).

Update: I’m listening to the closing talk by Langlands. He is explaining his version of geometric Langlands, responds to criticism from Frenkel with “As far as I know there are no errors in the paper, no matter what you may see elsewhere”. He ends his talk with something like “At the last page I threw down my pen… It works and it works by a miracle. Don’t doubt it, it does work!”

Update: Another livestream, starting in moments: Alice and Bob Meet the Wall of Fire, a panel discussion with Quanta writers at the Simons Foundation.

Update: Videos from the Langlands Abel conference are now available, in particular Frenkel here and Langlands here.

Update: For another expository piece about the Langlands program, one that I somehow missed when it came out recently, see Sol Friedberg’s What is the Langlands Program? in the AMS Notices.

Update: An updated version of Frenkel’s notes is now available at the arXiv. Highly recommended for its lucid explanation of the form the geometric Langlands program has taken.

Posted in Langlands, Uncategorized | 14 Comments

Updates

Posted on November 1, 2018 by woit

Based on this preprint from Banks and Fischler, I added an update to the FAQ entry about why the ever-popular “string theory makes predictions, but only at high energies where they can’t be tested” argument is not true.

This preprint also updates the acknowledgments story discussed here, with the current version:

The work of T.Banks is NOT supported by the Department of Energy, the National Science Foundation, the Simons or Templeton Foundations or FQXi. The work of W.Fischler is supported by the National Science Foundation under Grant Number PHY-1620610.

Posted in Uncategorized | Comments Off on Updates

Langlands News

Posted on October 30, 2018 by woit

Various Langlands program related news, starting with the man himself:

  • For the latest from Langlands about the geometric theory, best if you read both Russian and Turkish. In that case you can read this and this. For the rest of us, all we get are this commentary on the Russian and Turkish documents and these last or very well last thoughts on them.
  • In a couple of weeks there will be a conference celebrating the work of Langlands, organized in conjunction with his Abel Prize. Perhaps there will be live stream here.
  • I hear that at his lecture at the CMI at 20 conference Scholze made some new conjectures about possible ways of getting the Langlands correspondence in certain cases of the number field case. I haven’t however seen anywhere that one can read or hear more about these. It would be great if the Clay Mathematics Institute could make available videos of the talks at that conference.
  • Scholze will be giving the Chow lectures in Leipzig next week. The program there includes some preparatory talks by others, including my ex-Columbia colleague Daniel Litt (now at the IAS). I see that Daniel has at least posted a problem set you can get started on.
  • Also coming up next week is the Breakthrough Prize Symposium at Berkeley, where Vincent Lafforgue will talk about his (valued at $3 million) work on the Langlands program Monday morning (live stream here). On the physics side, in the evening a group of prize-winning theorists will talk about “Is Time Travel Possible”, live stream here.
  • A central idea conjecturally relating the geometric version of local Langlands to the number field version is the Fargues-Fontaine curve, which Jacob Lurie has been giving a course about at Harvard UCSD this fall.

    This fall in Bangalore there will be a meeting devoted to the Fargues-Fontaine curve, about which the organizers tell us: “This field will unravel in the coming years…”

  • On the local geometric Langlands front, there’s something new from Dennis Gaitsgory. I’ve always been fascinated by the way BRST appears in this story.
  • I’m told by experts that one of the best recent results in the Langlands program is this work, which doesn’t seem to have yet made it to the arXiv, but was explained in some detail in a blog post last year by Frank Calegari.

Update: Slides from the Chow Lectures are becoming available, see here. Remarkable in particular is Peter Scholze’s wonderful introductory lecture on Numbers and geometry, which includes something one sees all too rarely, a set of drawings showing the sort of pictures arithmetic geometers have in their minds for how to think about number theory geometrically.

Update: I just watched Vincent Lafforgue’s talk at the Breakthrough symposium. It included basically thanks to the CNRS for providing him a permanent position with freedom, a survey of Langlands, mainly talking about the topology of algebraic varieties, and comments on the ecological crisis. He says he’ll put up the slides on his website
http://vlafforg.perso.math.cnrs.fr/

He made one (to me) very striking claim, that the functoriality conjecture could be thought of as a quantization problem, how to pass from a classical system to a quantum system. Can an expert enlighten me on what exactly he was referring to here?

Update: Lafforgue’s slides are here. James Milne has provided a Google-translated version of the Langlands Russian article here, with the comment:

This may help readers gain some idea of what the manuscript is about until there is an official translation. Given that even native Russian speakers (not just google) have trouble understanding Langlands’s Russian, this would best be done by the author.

Update: Edward Frenkel gave a talk at the Langlands Abel Prize conference discussing the geometric theory and a bit about recent ideas of Langlands on this topic. He has written up some detailed notes on his take on this, available here.

Update: Videos of the CMI-20 talks are available, with Scholze’s here.

Posted in Langlands | 11 Comments

The End of LHC Run 2 and the Road Ahead

Posted on October 24, 2018 by woit

Some experimental HEP news items:

  • Since 2015 the LHC experiments have been taking data from proton-proton collisions at 13 TeV. This is “Run 2” of the LHC, “Run 1” was at the lower energy of 8 TeV. The proton-proton Run 2 ended this morning, with the LHC shifting to other tasks, first machine development, later heavy ions. It will shut down completely in December for the start of “Long Shutdown 2 (LS2)”, which will last for over two years, into early 2021. During LS2 there will be maintenance performed and improvements made, including bringing the collision energy of the machine up to the design energy of 14 TeV.

    ATLAS is reporting 158 inverse fb of collisions delivered by the machine during Run 2, of which 149 inverse fb were recorded, the CMS numbers should be similar. Most data analysis reported to date by ATLAS and CMS has only used the 2015 and 2016 data (about 36 inverse fb) although a few results have included data through 2017 (about 80 inverse fb). My impression is that for many searches they have been waiting for the full run 2 dataset to be available. Perhaps results of searches with the full dataset might start becoming available by the time of summer 2019 conferences.

    The LHC run 3 is planned for 2021-2023, producing perhaps 300 inverse fb of data, results perhaps available in 2024. It will thus be quite a long time after run 2 results start appearing before better ones due simply to more data become available.

  • The Europeans are now starting a process that will lead to an update of the
    European Strategy for Particle Physics. Tommaso Dorigo has a blog post here, and there’s a website here. A first stage of this process will ask for community input, with deadline December 18, via a portal that will open November 1. The next stage will be an Open Symposium to be held May 13-16 in Granada.
  • This week there’s a Workshop on Future Linear Colliders being held in Austin Texas. The big question being discussed there is whether the Japanese will decide to go ahead with a plan to build the ILC, a 250 GeV linear electron-positron machine. The current situation is described in detail here, with the crucial next step a decision from the Science Council of Japan expected by the end of November. If the ILC project does go forward, a tentative schedule has construction beginning in 2026 and commissioning in 2034.
  • For a theorist’s recent take on future colliders, see this from LianTao Wang. One thing Wang reports is an “excuse to have fun” (since it’s based on an unrealistic assumption), a community study in particle theory being organized by Michael Peskin, which would address the question “What would we learn from an electron accelerator of energy 10-50 TeV?”
Posted in Experimental HEP News | 34 Comments

Last Night’s Hype

Posted on October 18, 2018 by woit

If you’re a Friend of the IAS ($1750/year and up), you were invited to a talk last night, at which IAS member Thomas Rudelius promised to explain to you How to Test String Theory. The video of the talk is now available here.

After a long introduction involving large amounts of misleading hype, Rudelius in the last couple minutes finally gets to the promised explanation of “How to Test String Theory”. What is it? It’s his discovery that some versions of axion cosmology are incompatible with the Weak Gravity Conjecture, and thus conjecturally incompatible with string theory.

I assume that the IAS Friends in attendance, besides being financially well off, are also not so dim-witted that they wouldn’t notice that they’d been had (there’s no evidence for axion cosmology, so conjectures about whether or not various axion cosmology models are consistent or not with string theory are completely irrelevant to “testing string theory”). Any questions asked after the talk didn’t make it to the video, so it’s unclear if anyone bothered to complain about what had just been done to them.

Update: For a sensible, informative video about string theory (as opposed to the IAS one), see this from Sabine Hossenfelder.

Posted in Swampland, This Week's Hype | 3 Comments

Breaking News

Posted on October 17, 2018 by woit

Two midday breaking news items:

  • The ACME II experiment is reporting today a new, nearly order of magnitude better, limit on the electric dipole moment of the electron:
    $$|d_e|\leq 1.1 \times 10^{-29} e\ cm$$
    The previous best bound was from ACME I in 2014:
    $$|d_e|\leq 9.4 \times 10^{-29} e\ cm$$

    One significance of this is that while the SM prediction for the electron EDM is unobservably small, generically extensions of the SM predict much larger values. Already the 2014 bound was in conflict with typical SUSY models with LHC-scale supersymmetry, and was starting to rule out parts of the ranges expected for split-SUSY models (Arkani-Hamed’s current “best bet”) as well as the expected range for SO(10) GUTs (see for instance slide 25 here).

    Today’s result pretty much completely rules out generic versions for both the most popular SUSY models still standing (Split SUSY), as well as the most popular class of GUTs. This provides another nail in the coffin of the SUSY-GUT paradigm which has dominated expectations for physics beyond the SM over the past forty years.

  • The Breakthrough Prize people are having their usual sort of ceremony for the 2019 prizes on November 4, with an Oscars-like production, this year hosted by Pierce Brosnan. In a break with the past, this year they’re announcing the winners in advance, see here. The $3 million physics prize goes to Kane and Mele for their work on topological insulators.

    The $3 million mathematics prize goes to Vincent Lafforgue, for his work on the Langlands correspondence. The prize description has some information about him I was unaware of:

    Deeply concerned about the ecological crisis, Lafforgue is now focused on operator algebras in quantum mechanics and devising new materials for clean energy technologies.

Update: The promotional videos for the Breakthrough Prize winners that will be shown at the November ceremony are already available on Youtube.

Update: Those phenomenologists work fast! A detailed study of the implications of the ACME result for SUSY models is on the arXiv tonight. For a precise version of the crude claim that “generic split SUSY is now ruled out”, look at the top two plots in figure 4.

Posted in Uncategorized | 9 Comments

This Week’s Hype

Posted on October 15, 2018 by woit

The story of string theory as a theory of everything has settled into a rather bizarre steady-state, with these three recent links providing a look at where we are now:

  • At his podcast site, Sean Carroll has an interview with string theorist Clifford Johnson. It’s accurately entitled What’s So Great About Superstring Theory, since it’s an hour of unrelenting propaganda about the glories of string theory, save for a short mention that there had been some criticism from (unnamed) sources a decade or so ago.

    The truly odd thing about the discussion though was the way it seemed frozen in time back in 1998 just after the advent of AdS/CFT duality, with almost no discussion of developments of the last twenty years. Nothing about the string theory landscape and the controversy over it, nothing about the negative SUSY results from the LHC. The attitude of Carroll and Johnson towards the failure of string theory unification seems to be to simply refuse to talk about it, and try to keep alive the glory days just after the publication of The Elegant Universe. They’ve taken to heart the post-fact environment we now live in, one where if you keep insisting something is true (string theory unification is a great idea) despite all evidence, then for all practical purposes it is true. Johnson has famously admitted that he refuses to read my book or Lee Smolin’s. As far as he’s concerned our arguments do not exist, and Carroll goes along with this by not even mentioning them.

  • For the latest on the Swampland (for background, see here), there’s String Theorists’ Heads Bobble Over Potential Dark Energy Wobble, where we’re told that string theorists are claiming “huge excitement” over the possibility that string theory might make a “prediction” about dark energy. Over the years there have been endless claims about “predictions” of string theory, none of which have ever turned out to actually exist, and this is just one more in that long line. The rather odd aspect of this latest prediction is indicated by how it is described in the last paragraph of the article:

    The real excitement comes from how soon we might know whether Vafa’s work has produced a testable prediction of string theory—which would be a first. Experiments like the Dark Energy Survey or the upcoming WFIRST telescope could possibly detect whether dark energy is constant or changing over time, and could perhaps do so within the next few years.

    Reading this, one gets the impression that we’ll know what string theory “predicts” about dark energy just when there’s a measurement. This actually does describe what’s going on here: for some, string theory is a theory of everything as a matter of faith, so to them any new measurement tells us more about string theory, in particular that string theory “predicts” that measurement.

  • Finally, there’s an article out by Thomas Hertog, which contains more about his work with Hawking that was widely advertised after Hawking’s death (see here). Hertog claims another sort of “prediction” of string theory:

    String theory predicts that our universe is fundamentally a hologram that reveals itself only in the most extreme conditions, such as those at the Big Bang.

    For the implications of this prediction, see String Theory Summarized.

Posted in Swampland, This Week's Hype | 14 Comments

High Life

Posted on October 3, 2018 by woit

I spent yesterday night at the New York Film Festival, watching Claire Denis’s new film High Life. For a detailed and accurate review of the film, see the one at Variety.

This film is about a voyage to a black hole, in some sense an anti-Interstellar. Where the scientific plot of Interstellar was inspirational and made no sense at all, in High Life you get a plot that is all too plausible, and completely depressing. There’s a spaceship headed on a mission to a black hole, but this one doesn’t have brilliant scientists, traveling in a clean and shiny environment, and out to save the world. Instead, the crew is a bunch of ex-Death Row inmates, stuck on a dead-end trip in a filthy spacecraft swarming with recycled excrement, being subjected to grotesque sexual experiments, with periodic violent assaults, murders, and screaming babies to liven things up.

The supposed mission of the spacecraft is to travel to a nearby black hole and test whether energy can be extracted by the Penrose process. Because of all the murdering and such, that doesn’t work out too well. The ending involves another trip into a black hole, with discussion of whether they’re going to hit a “firewall”. One character thinks not, but that sure looks like one to me at the end. Theorist Aurélien Barrau is listed as “Cosmic Companion” or some such, and must have been responsible for providing the higher level of scientific verisimilitude than that of Interstellar (one of the images of a black hole does look like the famous one Kip Thorne provided for the earlier film).

I can’t really recommend this film to the average viewer seeking enlightenment or entertainment. On the other hand, if you’re looking for something unrelievedly grim, grotesque and disturbing, and really like black holes, maybe you should check it out.

Posted in Film Reviews | 15 Comments

Various and Sundry

Posted on September 28, 2018 by woit

First, news related in some way to Australia:

  • This summer the Sydney Morning Herald published a nice profile of Geordie Williamson.
  • By the way, the ICM plenary lectures are finally available on video, with Williamson’s among those worth watching.
  • The Sydney Morning Herald also recently had an article on quantum computing, motivated by a public talk by Patrick Hayden. The opening lines of the piece contain a classical superposition of quantum hype:

    Quantum computing will be so advanced that it will make your desktop computer look like an abacus, says Stanford University professor Patrick Hayden.

    However Professor Hayden, who will present a public lecture in Sydney on Wednesday, is keenly aware that “the hype is just out of control at the moment”.

Among talks I wish I’d gotten to see or am sorry I won’t be able to attend, there’s

If you just can’t get enough of the debate over string theory:

On politics and quantum theory:

  • I learned today from the Economist that the President of Armenia, Armen Sarkissian, is a theoretical physicist. Early in his career he worked in general relativity, see here. The Economist has Sarkissian promoting the idea of “quantum politics”:

    In his view, our interpretation of how politics traditionally works should be updated to reflect the way that physics has been reimagined. The classical world of post-Newtonian physics was linear, predictable, even deterministic. By contrast, the quantum world is highly uncertain and interconnected and can change depending on the position of the observer.

    “A lot of things in our lives have quantum behaviour. We are living through a dynamic process of change,” he says. “I think we have to look at our world in a completely different way.”

    I have no idea what’s going on in Armenian politics and whether quantum theory is the way to understand it. As for the current horror-show that is US politics, one thing that doesn’t deserve the blame for it is quantum theory.

A very quick mini-book review:

  • I just got a copy of Alvaro de Rújula’s Enjoy Our Universe, which is a short and entertaining, colorfully illustrated, overview of the current state of of high energy physics and the universe. The book brings back fond memories of a late-seventies course on particle physics that I took from de Rújula, whose humorous and lively character comes through in the book. For instance, about credit for discoveries:

    There is increasingly convincing evidence that the Vikings set foot in America as early as the tenth century. There is no question that the Amerindians were there much before that. And yet, the glory of “discovering” America goes to Columbus. Thus, the point is not being the first to discover something, but the last.

    About the relation of theory and experiment (this comes with a hand drawn illustration):

    In particle physics, discoveries – serendipitous or not – are generally made by experimentalists, in astrophysics and cosmology by observers. In both cases there are also the theorists. High time to explain the distinctions. This is done in Figure 53. The question is what the similarities between the two sets are. One set consists of a farmer, his pig, and the truffles, the other of the theorist, the experimentalist (or the observer), and the discoveries. The farmer takes his pig to the woods. The pig sniffs around and discovers a truffle. The farmer hits the pig with his bat and takes the truffle away. These are the similarities. The difference is that the theorist scarcely ever directs the experimentalist to woods where there are truffles.

    Beside the humor, the book is mostly succinct, clear and profusely illustrated explanations of important physics and astrophysics. The author early on explains that he plans to avoid discussing the sort of speculation popular in many other books, with a footnote justifying this:

    There is nothing wrong in discussing these subjects, except, in my opinion, doing it without a very clearcut distinction between facts, reasonable conjectures, and outright fantasies.

Update: Some news and views on an open access development, courtesy of Mark Hillery:

  • “Plan S has been put forward by a consortium of European funding agencies, including those of the UK, France, and the Netherlands, though not, as of now Germany, and it would require recipients of their funding to publish in gold open-access journals or vaguely defined compliant open access platforms by 2020. Hybrid journals, such as the Physical Review, will not be allowed. Gold open access requires that authors pay to have their papers published. The claim is that a cap on article processing charges (APC’s) will be mandated, but the details have not been spelled out yet. More information can be found here.

    http://www.sciencemag.org/news/2018/09/european-science-funders-ban-grantees-publishing-paywalled-journals

    A good discussion of open access can be found here.

    https://otwartanauka.pl/in-english/experts-on-open-access/open-access-will-remain-a-half-revolution-interview-with-richard-poynder

    This is an attempt to force the gold open access model on all of scientific publishing. In a rebuttal to Plan S,

    Response to Plan S from Academic Researchers: Unethical, Too Risky!

    a group of young European researchers has pointed out that it would prohibit them from publishing in 85% of existing journals. They also point out a number of additional problems with Plan S.
    1. While anyone can read an article in a gold open access journal without charge, publishing in one is a different story. APC’s, or what used to be known as page charges, are typically several thousand dollars per article. This seriously restricts the pool of people who can publish is such journals.
    2. What happens if the rest of the world does not go along with Plan S? Collaborations between EU and non-EU researchers would not be able to publish their results in many high-impact journals (Physical Review Letters, for example), and this could discourage such collaborations. It should be noted that Robert-Jan Smits, the Open Access Envoy of the European Commission, is tying to persuade funding agencies in North America to join in Plan S.
    3. Telling people where they can publish violates academic freedom.
    4. In a gold open access journal, the financial incentives favor publishing lots of papers; the more papers published, the greater the income of the journal. This could lead to quality problems.
    The rebuttal also points to possible alternatives to Plan S, such as green open access, which would allow a researcher to deposit a version of their paper in an online depository, such as the arXiv, at the time of submission and then submit the paper to a journal of their choice.

    While I am not a fan of commercial scientific publishers, whose profit margins are ridiculous, I am a fan of society journals (I work part time for one, Physical Review A). These journals are reasonably priced, and income from them helps support societies, such as the American Physical Society, and their activities. Plan S is a bureaucratic attempt to impose, from the top, a publishing model on the world with which many people disagree or have grave reservations.”

Posted in Book Reviews, Uncategorized | 30 Comments

Scholze and Stix on the Mochizuki Proof

Posted on September 20, 2018 by woit

As discussed here a couple months ago, Peter Scholze and Jakob Stix believe they have found a serious problem with Mochizuki’s claimed proof of the abc conjecture, and traveled to Kyoto in March to discuss it with him. Their write-up is now available here. Mochizuki has made public his response to this, creating a web-page available here. There’s also an updated version of Ivan Fesenko’s take on the story, as well as a possibly relevant FAQ on IUTeich from Go Yamashita.

Erica Klarreich has an excellent long and detailed article about this story at Quanta.

Update: Looking through these Scholze/Stix/Mochizuki documents, my non-expert opinion is that Mochizuki does not seem to effectively address the Scholze-Stix objections, which are aimed at a very specific piece of his argument. Unfortunately, he also does his own credibility a huge amount of damage by including over-the-top attacks on the competence of Scholze and Stix, in typefaces that make him look unserious. For instance, there’s

I can only say that it is a very challenging task to document the depth of my astonishment when I first read this Remark! This Remark may be described as a breath-takingly (melo?)dramatic self-declaration, on the part of SS, of their profound ignorance of the elementary theory of heights, at the advanced undergraduate/beginning graduate level.

or the last couple pages of his report.

Update: More of the same about IUT from Fesenko available here. His argument is that the overwhelming majority of leading experts in arithmetic geometry who are skeptical of the purported abc proof should be ignored, since they haven’t put in the two years of continuous study of IUT necessary. I don’t think this collection of ad hominem arguments will do anything to change anyone’s mind. I also don’t see why he doesn’t instead produce what could change minds: a clear and convincing technical refutation of the Scholze-Stix argument.

Posted in abc Conjecture | 37 Comments