Two more items:

- I can’t recommend strongly enough that you watch the new Curt Jaimungal podcast with Edward Frenkel. The nominal topic is the recent proof of the geometric Langlands conjecture, but this is introductory material, with geometric Langlands and the proof to be covered in a part 2 of the conversation.
Before getting into the story of the Langlands program at a very introductory level, Frenkel covers a wide range of topics about unification in math and physics and the difference between these two subjects. While there’s a lot about mathematics, Frenkel also gives the most lucid explanation I’ve ever heard of exactly what string theory is, what its relation to mathematics is, and what its problems are as a theory of the real world. He has been intimately involved for a long time in research in this field, playing a major role in the geometric Langlands program and working together with both Langlands and Witten.

- Nordita this month is hosting a program on quantum gravity, aimed at covering a diversity of approaches. Videos of the talks are appearing here. The program includes an unusually large number of panel discussions about the state of the subject. One of these is a discussion of the Status of the string paradigm which has the unusual feature that two string theory skeptics (Damiano Anselmi and Neil Turok, who have worked on string theory) have been allowed to participate in the six member panel.
The response to the failures over the last forty years seems to be that current researchers should not be held accountable for ways in which the string theory paradigm of the past has not worked out. Things are fine now that they have moved on to the Swampland program, have realized that progress on string theory will have a 500 year time-scale, and know that string theory is better than the Standard Model since it has a finite or countable number of ground states.

What a marvellous podcast with Edward Frenkel! I think the host was getting frustrated that Frenken stayed at an elementary level in his explanation, but what a blessing this was for non-mathematicians like me. His introductory digression into string theory was also amazing (with hilarious reference made to Archimedes – yes jump out of the bath and run around naked, but not for 40 years).

Would you say that the connection between geometric Langlands and S-duality is a curiosity or that it hints at something larger and of greater use?

Some guy idk,

Definitely this is a reflection of something deep about math and physics that we don’t fully understand. For what is understood, Frenkel is a great source, I also recommend looking at David Ben-Zvi’s talks and lecture courses on the subject.

Though I find Jaimungal a bit overbearing at times (e.g. the occasional melodramatic background music) I also find great value in what he does, particularly for retired generalist geezers like me who no longer keep up with the cutting edge of research in any area. And I have to agree that the interview with Frenkel was a total revelation. Frenkel’s depth of knowledge and philosophically cogent views re. Mathematics, Physics, and Mathematical Physics, combined with his humor and common sense are a truly rare gift. I found it amazing that in that relatively short presentation I finally attained some insight into why proving Taniyama-Shimura-Weil in turn proved Fermat’s Theorem as well as things like what’s so important about N=4 supersymetry (maximally consistent extension of the Poincaré group). I wait with bated breath for the geometric Langlands conclusion !

They proved geometric Langlands. They soaked the metaphorical nut to the maximum. Now we must apply their technologies and hammer and chisel away at arithmetic Langlands until nothing is left.

Karl Young writes:

“Though I find Jaimungal a bit overbearing at times”

Maybe. But Frenkel would get stuck on a point and not move on, and Jaimungal would pull him back on track. Sure, I found myself disagreeing occassionally, but overall, he did a great job.

“particularly for retired generalist geezers like me”

Exactly. The magic of Frenkel is that he shows us non-specialists what we need to be looking into to get one step deeper into the material.

This is the opposite of a common complaint I have with Quanta math articles: it’ll say “a bit is a thing that can take on one of two values” and then jump into bleeding-edge-level math without showing you how to get there.

@C

It’s important to note that they only proved unramified geometric Langlands. The unramified geometric Langlands conjecture is often called the geometric Langlands conjecture because the ramified version is harder to state, and most work has been in the unramified case, but I would still guess that proving ramified geometric Langlands is easier than proving the function field Langlands conjecture, which is easier than proving the reciprocity conjecture for representations algebraic at infinity in the number field case, which is easier than proving the full Langlands conjectures over number fields.

I’m probably a first-time commenter here, but a long-time reader. Unlike the rest of the comments prior to mine, I wanted to thank you for sharing details of the Nordita program. I began with Status of the String as you recommended. I found the panel contributions of the two former string theorists (Damiano Anselmi and Neil Turok) to be the most informative and accessible. Anselmi presented first; too bad he was halved and even quartered in the video, all the way to the left of the screen. Turok didn’t mince words, nor was he sarcastic! Both did good Q&As.

Slightly off-topic: In the Wikipedia entry for Not Even Wrong, a few outgroup editors–myself included–have been trying to include mention of this blog. Not Even a single sentence has been allowed. Amusingly, the same editors who are the most anti-theist (their recent Wikipedia initiative was to categorize all Hindu deities, the Christian trinity, and G-d and the prophets of Judaism as “in-world characters”) are also the most ardent supporters of unprovable physics.

Frenkel must be a lot of fun to interview. I’ve really enjoyed hearing his thoughts on these and other subjects that are now available online.

It’s tough to not get a bit discouraged, despite his jovial attitude. Insuperably large numbers of Calabi-Yau manifolds and the moduli stabilization problem are literally decades-old issues. It’s nice to have it summarized so succinctly, but he could have provided exactly the same assessment 20 years ago, as others did, and have been doing. Yet today we have the Swampland Conjectures, one of which flatly denies our universe is what precision cosmology (which today is a fair term) tells us.

The basic fact is that String Theory (with a capital S, I suppose) has been in violent disagreement with observation from the beginning, which is an astonishingly long time for anything remotely resembling science to be allowed to persist. That really is the bottom line, and philosophical arguments about beauty and the validity of anthropic reasoning, etc., etc. ad nauseam, should really have been minor asides to the basic, glaring fact of the matter: These ideas are just incredibly empirically wrong. They always have been, and there’s precisely zero justifiable reason to think by now they won’t always be.

Occasionally this lands again on my brain like a physical blow, and I’m just bewildered again. You’d think by now I’d be inured to the disillusionment, especially given the state of the world at large, but afraid I’m not there yet.

LMMI,

What’s discouraging are the many influential people in this subject who, forty years later, still promote the same hype. The interviews with Susskind and Frenkel are encouraging in that more and more people who understand this subject are willing to speak up and acknowledge that things haven’t worked out.

Almost on cue, Quanta comes out with an article suggesting the putative DESI anomaly is support for the Swampland program. Ambulance chasing with a heap of grossly exaggerated relevance. My disillusionment continues unabated.

Dear Peter, thanks for the interesting and useful links (as always).

Let me start with a consideration on the quantum gravity program in Nordita: “(non-commutative) geometry” was essentially absent from the panorama of the many approaches to quantum gravity covered there. This is not surprising at all: (as I already mentioned here in comments to previous posts) it is already several years that approaches based on “geometry” somehow disappeared from the current trends in QG where, across all the several lines of research, there is a uniform substantial agreement on the fact that “geometry” is only *emergent* and the fundamental degrees of freedom are quantum *pre-geometric*. The main trouble for researchers that try to dedicate time and energy on the study of *geometry of QFT* in view of applications to QG (including spinorial/twistorial geometry in 4-d), is not so much now the hype due to string theory, holography or quantum information, but this kind of wide consensus that deprives general relativity (and geometry) from a role in a fundamental theory. This, in my opinion, is deeply related to the historical evolution of QFT “post-renormalization”, with its ideological reliance on “effective field theory”, reductionism and “emergence”.

Among the speakers/moderators invited in the several panel discussions in Nordita, I found particularly interesting N.Turok (with His intriguing alternative “mirror-cosmology”) and (in view of my personal lines of research in algebraic QFT in QG) the point of view of S.Giddings on the encoding of geometry via the net of observables algebras on Hilbert space … something that in algebraic quantum field theory goes back to R.Haag and U.Bannier (and was further developed, in view of reconstruction of Minkowski space-time, by D.Buchholz and S.Summers).

The podcast from Frenkel is for sure very pleasant: I do appreciate His great ability to simplify a very complicated topic in a way that still allows to grasp some fundamental ideas. Still, I suspect that “oversimplification” in the discussion about the relation between mathematics and physics is deeply misleading: it might serve as a naive explanation/justification for the huge past and present interest of some mathematicians in mathematical topics related to, or inspired by, string theory, but nothing more than that. The interplay between the notions of “mathematical truth” and “physical reality” is way more complex than the mere statement that physical reality is a singleton in a landscape of mathematical truths (that btw seems to suggest that mathematicians are living in a “delusion of imaginary landscapes”). Furthermore mathematics is not completely immune to the social pathologies created by hype and powerful influences that have been so evident in certain areas of theoretical physics: the role of “standard proofs” or “computer simulations” in mathematics is very similar to that of “reproducible experimental evidence” in physics and hence similar issues are going to be found when reliance on such pillars is shaking or just changing (see “theoretical-mathematics” as in Jaffe-Quinn or the current discussions on “automated theorems checking and AI” as exposed in the recent Scientific American interview to T.Tao or in M.Harris’ blog).

Best Regards 🙂

Reading the program on Quantum Gravity : the title of the second week Workshop on

FormalAspects and Consistency of Quantum Gravity Approachesreminds me of the following quote of Pierre Cartier (who died a few days ago*)source: https://www.emis.de/journals/SLC/wpapers/s44cartier1.pdf

His death is a loss for the mathematical community I think from my narrow perspective as he was a bridge between mathematicians and mathematical physicists if not theoretical physicists and mathemagicians.

It might be worth noting his dream of a cosmic Galois group is still alive and a kicking example of hopes and dangers or subtleties in conjectures illustrated for instance by Francis Brown work on multizetas or Elliott Gesteau last preprint on the factorization paradox.

*https://www.lemonde.fr/disparitions/article/2024/08/19/pierre-cartier-mathematicien-francais-est-mort_6286756_3382.html