This Week’s Hype

Posted on September 8, 2021 by woit

Today Quanta has One Lab’s Quest to Build Space-Time Out of Quantum Particles. No, this kind of experiment is not going to “Build Space-Time”, now or ever. This kind of obfuscation about quantum gravity advances neither fundamental physics nor the public understanding of it, quite the opposite. The article does make clear what the motivation is: deal with the problem that

String theory, still the leading candidate to replace the Standard Model, has often been accused of being untestable.

by claiming that it somehow can be tested in a lab.

Posted in This Week's Hype | 17 Comments

Conversations on Quantum Gravity

Posted on August 26, 2021 by woit

Things for many years now have been going badly for string theory on the public relations front. Today the Economist has Physics seeks the future: Bye, bye, little Susy, where one finds out that:

But, no Susy, no string theory. And, 13 years after the LHC opened, no sparticles have shown up. Even two as-yet-unexplained results announced earlier this year (one from the LHC and one from a smaller machine) offer no evidence directly supporting Susy. Many physicists thus worry they have been on a wild-goose chase…
Without Susy, string theory thus looks pretty-much dead as a theory of everything. Which, if true, clears the field for non-string theories of everything.

Unfortunately for the public understanding of science, this is followed by

But at the moment the bookies’ favourite for unifying relativity and the Standard Model is something called “entropic gravity”… in the past five years, Brian Swingle of Harvard University and Sean Carroll of the California Institute of Technology have begun building models of what Dr Verlinde’s ideas might mean in practice, using ideas from quantum information theory.

For something much more anecdotal, on Saturday night I was having dinner outside in a hut during a rainstorm on the Upper East Side (having fled an aborted Central Park concert), and started talking to a couple seated nearby. When informed I taught math and did physics, one of them recommended Carlo Rovelli’s new book to me, and said he hoped I wasn’t doing string theory. Luckily I could reassure him about that.

This morning I found out about Conversations on Quantum Gravity, a fascinating book published by Cambridge that appeared online today, hard copies for sale in November. It consists of interviews about quantum gravity put together by Dutch string theorist Jay Armas, starting in 2011. The scale of this project is immense: there are 37 interviews, most of them rather long and detailed, making up a book of 716 pages. What I’m writing here is based on a day’s worth skimming of the book. I’ll likely go back again and look more carefully at parts of it.

Roughly half the interviewees are string theorists, with the author making a concerted effort to also include non-string theory approaches to quantum gravity. I made the mistake of starting off by reading some of the string theorist interviews, which was rather depressing. By the end of the day, after making my way through about 20 long interviews with string theorists, with few exceptions the story they were telling was one I’m all too familiar with. It’s roughly

We don’t actually know what string theory is, just that it’s a “framework” that encompasses QFT and much more. We can’t predict anything with it now and don’t see any plausible way of predicting anything in the future, but the theory is a successful theory of quantum gravity, unlike our competition. There is no good reason for people to be working on anything else.

For example, here’s Cumrun Vafa:

If a young student asks you what approach to quantum gravity they should work on, what would your answer be?

There is no question that string theory is the right framework to understand quantum gravity. By this I mean that it is closer to the truth than any other existent theory.

Is it worth exploring other approaches?

Well . . . certainly being close-minded is not good. We should be open to other developments. But the fact that there exist other subjects does not justify exploring them if they are not on equal footing with string theory.

and here’s Edward Witten:

Due to the lack of experimental data, there exist a plethora of different approaches to quantising gravity. Which of these approaches, in your opinion, is closer to a true description of nature and why?

I would say your premise is a little misleading. String theory is the only idea about quantum gravity with any substance. One sign is that where critics have had interesting ideas (non-commutative geometry, black hole entropy, twistor theory) they have tended to be absorbed as part of string theory.

and David Gross:

So you don’t think that other approaches like loop quantum gravity have . . .

Loop quantum gravity is total BS. I mean, it’s really not worth discussing it. Don’t put that in the book. But, it really isn’t.

Luckily Armas doesn’t take up Gross on the suggestion that loop quantum gravity is not worth discussing, interviewing quite a few people who are working on research programs that have grown out of it. I got much more out of these interviews, which were very different in tone and content than the ones with string theorists. Many of them gave a very clear account of the technical problems these approaches have encountered, referring to very specific well-defined models and calculations. Instead of the triumphalist claims and vague speculation of the string theorists there was a careful explanation of exactly what they were trying to do and the problems they were trying to overcome.

There’s a huge amount worth reading in these interviews, perhaps I’ll later add some more pointers. A couple specific examples that occur to me right now are Steve Carlip’s careful discussion of the quantization of the toy model of 2+1 dimensional gravity, and Lee Smolin’s very personal account of his frustration at the reception of his book “The Trouble With Physics”.

If your institution is paying Cambridge for access, you should take advantage of this now and take a look. Congratulations to Jay Armas for bringing us this material.

Update: There’s a new preprint out by historian of science Sophie Ritson, Constraints and Divergent Assessments of Fertility in Non-empirical Physics in the History of the String Theory Controversy, which examines in detail the arguments of the string wars and later over how to evaluate string theory. While I don’t think there’s a single reference in the 716 page Armas book to anything I’ve written, my views do make an appearance in this article.

Update: There’s a linked editorial in the Economist Fundamental physics is humanity’s most extraordinary achievement, which (rather optimistically) sees the current state of affairs as:

Supersymmetry is a stalking horse for a yet-deeper idea, string theory, which posits that everything is ultimately made of infinitesimally small objects that are most easily conceptualised by those without the maths to understand them properly as taut, vibrating strings.

So sure were most physicists that these ideas would turn out to be true that they were prepared to move hubristically forward with their theorising without experimental backup—because, for the first decades of Supersymmetry’s existence, no machine powerful enough to test its predictions existed. But now, in the form of the Large Hadron Collider, near Geneva, one does. And hubris is turning rapidly to nemesis, for of the particles predicted by Supersymmetry there is no sign.

Suddenly, the subject looks wide open again. The Supersymmetricians have their tails between their legs as new theories of everything to fill the vacuum left by string theory’s implosion are coming in left, right and centre.

Posted in Book Reviews | 42 Comments

Some Math Items

Posted on July 30, 2021 by woit

Some math items that may be of interest:

Update: The Scholze review has been removed (temporarily?). A cached version is here.

Update: The review was temporarily removed just because what was posted wasn’t a finalized version, this is explained here. They should repost once Scholze has a chance to make any final edits.

Update: The review is back up.

Update: Michael Harris has a new substack site, where he’ll be writing about the mechanization of mathematics. I’m glad to see someone doing this from his point of view.

Posted in abc Conjecture, Uncategorized | 8 Comments

More of the Same (Physics, Math and Unification)

Posted on July 29, 2021 by woit

I was going to just provide the following links with a some comments, but decided it would be a good idea to put them into what seems to me the larger context of where we are in fundamental physics and its relationship to mathematics.

For the latest on the conventional physics approach to unification (GUTS, SUSY, strings, M-theory), there’s:

  • The Lex Fridman podcast has an interview with Cumrun Vafa. Going to the section (1:19:48) – Skepticism regarding string theory) where Vafa answers the skeptics, he has just one argument for string theory as a predictive theory: it predicts that the number of spacetime dimensions is between 1 and 11.
  • A second edition of Gordon Kane’s String Theory and the Real World has just appeared. One learns there (page 1-19) that

    There is good reason, based on theory, to think discovery of the superpartners of Standard Model particles should occur at the CERN LHC in the next few years.

For the latest in mathematics and the interface of math and physics, there’s

About the first two links, I’m at a loss for words.

The second two are extremely interesting topics indicating a deep unity of number theory, geometry and physics. They’re also not topics easy to say much about in a blog posting. In the Fargues-Scholze case that’s partly because the new ideas they have come up with relating arithmetic and geometry are ones I don’t understand very well at all (although I hope to learn more about them in the future). The connections they have found between representation theory, arithmetic geometry, and geometric Langlands are very new and it will likely be quite a few years before they are well understood and their implications well-developed.

In the Gaiotto-Witten case, some of what they discuss is very familiar to me: geometric quantization has been a topic of fascination since my student days, and one major goal of my QM book was to work out in detail (for the case of $\mathbf R^{2d}$) some of the subtleties about quantization that they discuss. For co-adjoint orbits in Lie algebras, geometric quantization has a long history, and “brane quantization” may or may not have anything new to say about this. For moduli spaces of vector bundles on Riemann surfaces, and Hitchin moduli spaces of Higgs bundles on Riemann surfaces, “brane quantization” might come into its own.

There is a fairly short path now potentially connecting fundamental unifying ideas in number theory and geometry to our best fundamental theories in physics (and seminars on arithmetic geometry and QFT are now a thing). The Fargues-Scholze work relates arithmetic and the central objects in geometric Langlands involving categories of bundles over curves. These categories in turn are related (in work of Witten and collaborators) to 4d TQFTs based on twistings of N=4 super Yang-Mills. This sort of 4d QFT involves much the same ingredients as 4d QFTs describing the Standard Model and gravity. For some better indication of the relation of number theory to this sort of QFT, a good source is David Ben-Zvi’s lectures this past semester (see here and here). I’m hopeful that the ideas about twistors and QFT in Euclidean signature discussed here will provide a close connection of such 4d QFTs to the Standard Model and gravity (more to come on this topic in the near future).

Posted in Euclidean Twistor Unification, Langlands | Comments Off on More of the Same (Physics, Math and Unification)

Steven Weinberg 1933-2021

Posted on July 24, 2021 by woit

I heard this morning the news that Steven Weinberg passed away yesterday at the age of 88.  He was arguably the dominant figure in theoretical particle physics during its period of great success from the late sixties to the early eighties.  In particular, his 1967 work on unification of the weak and electromagnetic interactions was a huge breakthrough, and remains to this day at the center of the Standard Model, our best understanding of fundamental physics.

During the years 1975-79 when I was a student at Harvard,  I believe the hallway where Weinberg, Glashow and Coleman had offices close together  was the greatest concentration of the world’s major figures driving the field of particle theory, with Weinberg seen as the most prominent of the three.  From what I recall, in a meeting one of the graduate students (Eddie Farhi?) referred to “Shelly, Sidney and Weinberg”, indicating the way Weinberg was a special case even in that group.   I had the great fortune to attend not only Coleman’s QFT course, but also a course by Weinberg on the quantization of gauge theory.

Weinberg was the author of an influential text on general relativity, as well as a masterful three-volume set of textbooks on QFT.  The second volume roughly corresponds to the course I took from him, and the third is about supersymmetry.   While most QFT books cover the basics in much the same way, Weinberg’s first volume is a quite different, original and highly influential take on the subject. It’s not easy going, but the details are all there and his point of view is an important one.  When you hear Nima Arkani-Hamed preaching about the right way to understand how QFT comes out uniquely as the only sensible way to combine special relativity and quantum mechanics, he’s often referring specifically to what you’ll find in that first volume.

Besides his technical work, Weinberg also did a huge amount of writing of the highest quality about physics and science in general for wider audiences.  An early example is his 1977 The Search for Unity: Notes for a History of Quantum Field Theory (a copy is here). His 1992 Dreams of a Final Theory is perhaps the best statement anywhere of the goal of fundamental physical theory during the 20th century. His large collection of pieces written for the The New York Review of Books covers a wide variety of topics and all are well worth reading.

At the time of the 1984 “First Superstring Revolution”, Weinberg joined in and worked on string theory for a while, but after a few years turned to cosmology. In early 2002 he was one of several people I wrote to about the current state of string theory, and here’s what I heard back from him:

I share your disappointment about the lack of contact so far of string theory with nature, but I can’t see that anyone else (including those studying topological nontrivialities in gauge theories) is doing much better. I thinks that some theorists should go on pushing as hard as they can on string theory, and others should do something else, but it is not easy to see what. I have myself voted with my feet (if that is the appropriate organ here) and switched entirely to work in cosmology, which is as exciting now as particle physics was in the 1960s and 1970s. I wouldn’t criticize anyone for their choices: it’s a tough time for fundamental physics.

A couple years after that time, Weinberg’s 1987 “prediction” of the cosmological constant became the main argument for the string theory multiverse. This “prediction” was essentially the observation that if you have a theory in which all values of the cosmological constant are equally likely, and put this together with the “anthropic” constraint that only for some range will galaxy formation give what seem to be the conditions for life, then you expect a non-zero CC of very roughly the size later found. I’ve argued ad nauseam here that this can’t be used as a significant argument for string theory in its landscape incarnation. One way to see the problem is to notice that my own theory of the CC (which is that I have no idea what determines it, so any value is as likely as any other) is exactly equivalent to the string landscape theory of the CC (in which you don’t know either the measure on the space of possible vacua, or even what this space is, so you assume all CC equally likely). One place where Weinberg wrote about this issue is his essay Living in the Multiverse, which I wrote about here (the sad story of misinterpretation of a comment of mine there is told here).

Weinberg’s death yesterday, taking away from us the dominant figure of the period of particle theory’s greatest success is both a significant loss and marks the end of an era. His 2002 remark that “it’s a tough time” is even more true today.

Update: Scott Aaronson writes about Weinberg here, especially about getting to know him during the last part of his life.

Update: For Arkani-Hamed on Weinberg, see here.

Update: Glashow writes about Weinberg here.

Posted in Obituaries | 18 Comments

The Problem of Quantization

Posted on July 12, 2021 by woit

I’ve been watching Witten’s ongoing talks about geometric Langlands mentioned here, and wanted to recommend to everyone, mathematician or physicist, the first of them, on The Problem of Quantization (pdf here, video here, the question session is very worthwhile). For those very sensibly not interested in the intricacies of geometric Langlands, this talk is about the fundamental issue of “quantization”.

Hamiltonian mechanics gives a beautiful geometrical formulation of classical mechanics in terms of the Poisson bracket on functions, while quantum mechanics involves operators with non-trivial commutators. It was Dirac’s great insight that “quantization” takes functions to operators, taking the Poisson bracket to the commutator. In mathematician’s language, it’s supposed to be a unitary representation of the Lie algebra of the infinite dimensional group of canonical transformations of a symplectic manifold, so a homomorphism from functions with Poisson bracket to the Lie algebra of skew-adjoint operators on a complex vector space.

The problem with this is that you’d like to have an irreducible representation, but the only way to get this is to pick some extra structure on the symplectic manifold. The standard example is the phase space $\mathbf R^{2n}$, where you have to pick a decomposition into position and momentum coordinates. The state space will then be functions of just position, or just momentum. A different choice is to complexify, and look at functions of either holomorphic or anti-holomorphic coordinates. This choice is called a “polarization”. One aspect of the “problem” of quantization is that, given a phase space (symplectic manifold), there may not be an appropriate polarization. Or, there may be many different ones, with no obvious reason why they should give the same quantum theory.

Witten doesn’t mention one aspect of this that I find most fascinating. For relativistic quantum field theories the phase space is a space of solutions of a relativistic wave-equation. To get physically sensible results one must choose a polarization that distinguishes between positive and negative energy (or between functions which extend holomorphically in the positive or negative imaginary time direction).

In these lectures, Witten advertises a rather exotic quantization contruction, using (even for a finite dimensional symplectic manifold ) conformally invariant boundary conditions in a two-dimensional QFT. I’m not convinced that this is really a good way to deal with the case where what you’re doing is looking for representations of a finite-dimensional Lie algebra, but it’s plausible this is the right way to think about the geometric Langlands situation, where you’re trying to quantize a moduli space of Higgs bundles.

In the question section, someone asked about my favorite approach to this problem, essentially using fermionic variables and cohomology. This can be thought of in general as using spinors and the Dirac operator, with the Dolbeault operator a special case when the symplectic manifold is Kähler. Witten responded that he had only really looked at this in the Kähler special case.

Posted in Quantum Mechanics, Quantum Theory: The Book, Uncategorized | 11 Comments

Deterioration of the World’s Thinking About the Deepest Stringy Ideas

Posted on July 12, 2021 by woit

For quite a few years now, I’ve been mystified about what is going on in string theory, as the subject has become dominated by AdS/CFT inspired work which has nothing to do with either strings or any visible idea about a possible route to a unified fundamental theory. This work is very much dependent on choosing a special background, in tension with the idea that, whatever string theory is, it’s supposed to be a unique theory that relates all possible backgrounds. This issue came up in a discussion session at Strings 2021, and it turns out that others are wondering about this too. There’s this today from Lubos Motl:

Aside from more amazing things, the AdS/CFT correspondence became just a recipe for people to do rather uninspiring copies of the same work, in some AdS5/CFT4 map, and what they were actually thinking was always a quantum field theory, typically in D=4 (and it was likely to be lower, not higher, if it were a different dimension!) whose final answers admit some interpretation organized as a calculation in AdS5. But as Vafa correctly emphasized, this is just a tiny portion of the miracle of string/M-theory – and even the whole AdS/CFT correspondence is a tiny fraction of the string dualities.

This superficial approach – in which people reduced their understanding of string theory and its amazing properties to some mundane, constantly repetitive ideas about AdS/CFT, especially those that are just small superconstructions added on top of 4D quantum field theories – got even worse in the recent decade when the “quantum information” began to be treated as a part of “our field”. Quantum information is a legitimate set of ideas and laws but I think that in general, this field adds nothing to the fundamental physics so far which would go beyond the basic postulates of quantum mechanics…

When Cumrun correctly mentioned that the real depth of string theory is really being abandoned, Harlow responded by saying that there were some links of quantum information to AdS/CFT, the latter was a duality, and that was important. But that is a completely idiotic way of thinking, as Vafa politely pointed out, because string theory (and even string duality) is so much more than the AdS/CFT. In fact, even AdS/CFT is much more than the repetitive rituals that most people are doing 99% of their time when they are combining the methods and buzzwords of “AdS/CFT” and “quantum information”. Many people are really not getting deeper under the surface; they are remaining on the surface and I would say that they are getting more superficial every day.

According to Lubos, he’s not the only one who feels this way, with an “anonymous Princeton big shot” agreeing with him (hard to think of anyone else this could be other than Nima Arkani-Hamed):

There is a sociological problem – coming from the terrifying ideological developments in the whole society – that is responsible for this evolution. I have been saying this for a decade or two as well – and now some key folks at Princeton and elsewhere told me that they agreed. The new generation that entered the field remains on the surface because it really lacks the desire to arrive with new, deep, stunning, revolutionary ideas that will show that everyone else was blind. Instead, the Millennials are a generation that prefers to hide in a herd of stupid sheep and remain at the surface that is increasingly superficial…

So most of the stuff that is done in “quantum information within quantum gravity” is just the work of mediocre people who want to keep their entitlements but who don’t really have any more profound ambitions. As the aforementioned anonymous Princeton big shot told me, their standards have simply dropped significantly. The toy models in the “quantum information” only display a very superficial resemblance to the theories describing Nature. That big shot correctly told me that in the early 1980s, Witten was ready to abandon string theory because it had some technical problems with getting chiral fermions and their interactions correctly.

Harlow says that many of the people – who may be speakers at the annual Strings conference and who may call themselves “string theorists” when they are asked – don’t really know even the basics of string theory. And they can get away with it. Just like there is the “grade inflation” and the “inflation of degrees”, there is “inflation in the usage of the term string theorist”. Tons of people are using it who just shouldn’t because they are not experts in the field at all. Harlow said that many of those don’t understand supersymmetry, string theory etc. but it’s worse. I think that many of them don’t really understand things like chiral fermions, either. It’s implicitly clear from the direction of the “quantum information in quantum gravity” papers and their progress, or the absence of this progress to be more precise. They just don’t think it’s important to get their models to a level that would be competitive with the previous candidates for a theory of everything – like the perturbative heterotic string theory, M-theory on G2 manifolds, braneworlds, and a few more. They are OK with writing a toy model having “something that superficially resembles a spacetime” and they want to be satisfied with that forever.

I don’t want to start here an ad hominem discussion of Lubos and his often extreme and eccentric views. On the topic though of the devolution of string theory as a TOE to playing with toy models of AdS/CFT using quantum information, it seems quite plausible that not only the “anonymous Princeton big shot” but quite a few other theoretical physicists see the current situation as problematic.

Posted in Strings 2XXX | 9 Comments

Even More Langlands

Posted on July 6, 2021 by woit

Various news at least tangentially related to the Langlands program:

Posted in Langlands | 3 Comments

Strings 2021

Posted on June 21, 2021 by woit

Strings 2021 started today, program is available here. Since it’s online only, talks are much more accessible than usual (and since it’s free, over 2000 people have registered to in principle participate via Zoom). Talks are available for watching every day via Youtube, links are on the main page.

As has been the case for many years, it doesn’t look like there will be anything significantly new on the age-old problems of getting fundamental physics out of a string theory. But, as has also been the case for many years, the conference features many talks that have nothing to do with string theory and may be quite interesting. I notice that Roger Penrose, a well-know string theory skeptic, will be giving a talk on the last day of the conference next week.

Another series of talks that I took a look at and that I can recommend is Nima Arkani-Hamed’s lectures on Physics at Future Colliders at the ICTP summer school on particle physics. He never actually gets anywhere near discussing the topic of the title for the talks, but does give a very nice leisurely introduction to computing amplitudes for zero-mass particles. What he’s doing is emphasizing ideas that are often not taught in conventional QFT courses (although they should be). His second talk explains how to think of things in terms of classifying representations of the Poincare group, an old topic that unfortunately is often no longer taught (see chapter 42 of my QM textbook). His third talk emphasizes thinking of space-time vectors as two by two matrices (see section 40.4 of my QM book). This is a truly fundamental idea about space time geometry that gets too little attention in most physics courses.

Update: At String 2021, yesterday Nima Arkani-Hamed gave a talk on “Connecting String Theory to the Real World We See Outside Our Windows”, where he sometimes sounds like me, contrasting the pre-LHC claims of string theorists:

1. LHC will discover SUSY
2. String Theory Loves SUSY + Unification

to what they are saying now that the LHC has found no SUSY

CICADAS [i.e. crickets]. (Anyway, String Theory is mainly about Quantum Gravity).

He goes on to explain the “landscape philosophy”, which he sees string theorists (and himself) as now adopting. According to this philosophy, “connection to particle physics appear[s] hopeless/”parochial”/unimportant”. As a result, he sees the current situation as

  • String theorists are for the most part no longer actively pursuing connecting to particle physics of the real world.
  • Understandable as a short-term strategy
  • But in my view a real mistake in the long run…

One reason for this being a real mistake is that, divorced from input from the real world, theory becomes sterile:

Questions Posed by Nature are Vastly Deeper and more fruitful than ones we humans tend to pose for ourselves.

Unfortunately I don’t think Arkani-Hamed has any compelling argument against “string theory implies landscape implies nothing to say about particle physics”. He discusses the “swampland philosophy”, but gives as a challenge to theorists just making more precise the sort of empty question that this philosophy deals in (he asks whether D=9 SU(2021) to the power 2021 is in the swampland).

Update: In the final discussion section, Witten emphasizes that “What is string theory?” still has no answer, that we have “little idea what it really is”. He lists two main things we know about the supposed theory:

1. General string perturbation theory using 2d conformal field theory. He mentions that one basic problem with this is that there is no understanding of what happens in time-dependent backgrounds, so, in particular, this is useless for addressing the big bang, which is the one place people now point to as a possible connection to real world data.

2. AdS/CFT

He notes that to get at non-perturbative string theory we seem to need some more general understanding of quantum theories, going beyond the usual quantization starting with an action, and ends by saying maybe quantum information theory can help. In the discussion section, Vafa challenges him on this, saying he sees no indication that quantum information theory gives any insight into dualities he sees as the central aspect of the non-perturbative theory. Witten’s answer is that this was just a vague hope, that the duality ideas are now 25 years old, we haven’t progressed beyond them, need something new.

Posted in Strings 2XXX | 34 Comments

Various Math Items

Posted on June 6, 2021 by woit

Some math-research items:

  • Mura Yakerson has been doing a really wonderful series of interviews with mathematicians, available at her math-life balance web-page or Youtube channel. I’ve just started listening to some of them, including ones with Peter Scholze and Dustin Clausen (Clausen is John Tate’s grandson, the latest AMS Notices has a memorial article).
  • There’s a remarkable report out from Peter Scholze about the progress of the Liquid Tensor experiment. Back when I first heard about this, I figured it was a clever plot by Scholze to get other people to help with a very complicated part of a proof, by getting them to work out the details, with the excuse being that they would be doing a computer check of the proof. Seemed to me very unlikely you could check such a proof with a computer, but that by forcing humans to try to disambiguate things carefully enough in preparation for a computer proof, he’d get a human-checked proof. Looks like I was wrong.
  • For yet more Scholze news, the Fields Medal symposium this year will be devoted to his work.
  • Trying to find something of interest in math, that wasn’t Scholze-related, I noticed this site devoted to the case of Azat Miftakhov, where there will be an online Azat Miftakhov Day program. Foiled though on the Scholze front, since he’s a speaker there, talking about Condensed Mathematics.
  • The list of those giving plenary lectures at next years ICM is here.

Update: Kevin Hartnett at Quanta has a good new article up about quantum field theory and mathematics (an inexhaustible topic…)

Update: Also from the Simons Foundation, there’s a wonderful profile of my Columbia colleague Andrei Okounkov, who has been very active in bringing together mathematics and ideas from quantum field theory.

Update: Nature has a story about the Liquid Tensor Experiment.

Posted in Uncategorized | 17 Comments