Ordered from the more to less serious…
- On the geometric Langlands front, there’s video posted today of this talk by Dennis Gaitsgory. Michael Harris has already commented here about the local geometric Langlands conjecture in terms of 2-categories that Gaitsgory discusses. Today’s arXiv listings have a new paper on geometric Langlands by Witten, which begins with his version of a formulation relating the categorical point of view and quantum field theory.
I wrote recently here about a talk by Jacob Lurie that alluded to an explanation of this categorical equivalence for the simplest case of G invertible complex numbers (rather than the case of G a general semi-simple Lie group that Gaitsgory and Witten are discussing). I’m still far from being enlightened concerning that simplest case, but have learned a lot from Alexander Polishchuk’s Abelian varieties, theta functions and the Fourier transform which I take as treating the global versions of this equivalence. - Witten has been busy, with yesterday’s arXiv listings including a 429 page paper with Gaiotto and Moore (does anyone know of a longer hep-th paper that’s not a review article?). There’s also a companion shorter summary paper. The motivation here is again a categorical picture expressed in terms of quantum field theory models, but for more insight you’ll need to find someone more expert than me on this topic.
- Strings 2015 will be held in Bangalore in a couple weeks. Talks titles are now available, so you can see what the hot topics in the “string theory” community are. Of Gaiotto, Moore and Witten, only Witten will be speaking. Perhaps his talk on An Overview of Worldsheet and Brane Anomalies will shed some light on the 429 page paper.
- On the Mochizuki/abc front, hopes rest on a planned workshop at Oxford this December. Fesenko has circulated a letter about the workshop, which gives suggestions about how to approach the subject.
- Via Chandan Dalawat’s Google+ page I found out about this autobiographical piece by Misha Gromov. One thing it made clear to me is why I couldn’t get anything out of the couple times I’ve heard him lecture.
Being trivial is our most dreaded pitfall: you say stupid things, not original things, outrageously wrong things – all will be forgotten when the dust settles down. But if you pompously call a+b=c “Theorem” in your paper, you will be forever remembered as “this a+b guy”, no matter you prove bloody good theorems afterwords…
I was introduced to the idea on September 1st 1960 at the then Leningrad University when our analysis professor Boris Mikhailovich Makarov said to me after our first calculus class – he expressed this in somewhat metaphorical terms – that I should’ve kept my mouth shut unless I had something non-trivial to say.
Further encouraged by my teachers and fellow students, I tried to follow his advice and, apparently, have succeeded – I hear nothing disrespectful about my mouth for the last 10-20 years. Strangely, this does not make me feel a lot happier.
“Trivial” is relative. Anything grasped as long as two minutes ago seems trivial to a working mathematician.Another thought this raises is that I’ve just spent the last 3 years of my life writing something trivial…
- I really like Jordan Ellenberg’s suggestion of Cold Topics Workshops.
- Mathematics makes it into the Guardian with an article about mathematical modeling.
- With the LHC inactive, some LHC physicists have had to spend their time studying plots (trigger warning, and NSFW).
Update: One more, far more serious than anything above. Sabine Hossenfelder brings up an important and rarely discussed topic here.
I guess that most readers live in d=4, N=0 and will stop reading at the first line “This paper is devoted to the study of massive two-dimensional theories with (2,2) supersymmetry” unless somebody explains what is the physical relevance of the next 429 pages
I understand your long-standing opposition to string theory. I genuinely appreciate your many elucidations on the validity of the subject — especially as an outsider who has no skin in the game (apart from a large part of my physics education coming from Leonard Susskind, who obviously has his now-somewhat baggy skin in).
However: Not withstanding this sentence, it is grammatically improper to put phrase “string theory” in quotes. It’s clear that you (and everyone involved) agree that string theory actually exists, that people label themselves string theorists, and that those opposed to the topic know a string theorist when they see one. So it’s unnecessarily derisive to act like the phrase itself is in dispute. Even if all of these fulfilled criteria weren’t true, it is still incorrect to put jargon in quotes.
You seem to have plenty of ammunition to attack the content of string theory and those who practice it. So concentrate your fire where it is best applied: the content of your opponents’ beliefs and not the name of their community.
Drew Day,
The use of quotes wasn’t in any way intended as an attack on string theory or the string theory community, it was just a quick way of referring to the widely acknowledged fact (see the recent posting “A view from an ex-string theorist”) that the name “string theory” is now misleading since most “string theorists” aren’t working on strings (and avoiding making the tedious point that most talks at Strings 2XXX aren’t about strings). The name really is extremely misleading at this point, but of course I’ll keep using it until a better convention comes along. But I don’t see a good argument against sometimes adding the quotes in a context where noting that it’s no longer an accurate name is appropriate.
Note added: please, interesting comments about any of the different topics of the posting are encouraged, string theory wasn’t actually one of them.
Hi Peter,
On the (very serious) topic of Bee’s posting, I strongly encourage everybody to read the linked lecture below. It’s by a distinguished philosopher, Peter Railton, and was delivered at a meeting of the American Philosophical Association. It’s a very personal recounting of many things, but most relevant here is his discussion of his personal battles with depression and the continuing stigma attached to it in academia (and outside academia). He discusses depression starting on p.12 — the section titled “A fourth transition” — but the whole lecture is worth reading.
http://leiterreports.typepad.com/files/dewey-lecture-drs-rev1.pdf
CUPhil,
Thanks, but I’d rather not encourage a discussion here of the difficult topic of depression, outside of the context of the postdoc system that Sabine puts it in. And, in any case, better that people discuss the topic at her blog, since she has done an excellent job of raising the topic and addressing it.
What a disgusting attitude. I hope he was joking.
I have noticed that Witten has sort of a habit of writing really long “papers” that are actually books. Does anyone read them? I mean, if he wasn’t Witten and would bet nobody would. However, being the most influential leader of his field, perhaps there are crazy people who take the challenge? And who judges the usefulness of this kind of paper for the field? Or maybe I’m just being completely naive, so would really like to read an informed opinion to correct my ignorance…
I agree entirely with M. Peter, is there a way you could tell us what Witten is up to in graduate terms or Susskind lecture level stuff? What is the advance? What did he accomplish this time? Thanks.
Dr Woit linked the summary paper, which is beautifully written and 45 pages long. They state applications on page 2. Treat yourself, don’t cheat yourself.
Bernhard,
The length of the papers isn’t really problematic. These are very complex topics, and if you’re going to work out details, papers become very long. A shorter paper might be much worse, making it much harder for anyone interested to follow what is going on. There are a relatively small number of people I would guess following the details of many of these things. The time is long gone when just the fact that Witten was working on something brought huge numbers of people into a subject.
Another question is whether the motivation for such technical work is getting enough attention. In the case of geometric Langlands, Witten and others have over the years written up quite a bit of expository material. For this latest 429 page paper, the motivation to me is still somewhat obscure, maybe just because I haven’t had time to look more carefully at the summary paper. If there is good motivation for this work, I’m sure in the future we’ll see more papers explaining this motivation.
Perhaps 2d N=2 LG models and knot homology as motivations somehow leave the reader cold. The 2d/4d correspondence should not.
One of the most reputed scientists of our time writes a paper but all you have to say about it is that it’s too long? Now that’s as much trivial as one can get.
I knew that F Dolan died at a young age a number of years ago. I did not know that it was this way. The Hell with the post-doctoral system and the rest of it. It’s just not worth it. The abuse that’s described in commentaries on the same page is all too real. This is madness.
Eduardo Lira,
You don’t seem to have read the little I did say about it. I’m not of the opinion it’s too long, actually wish it were slightly longer, with a bit more explanation of the motivation of the work. If I understood that better I might have more to say (or maybe not, this was a posting intentionally of short items and links).
Dear jon, when Einstein started avoiding quantum mechanics, when de Broglie and Heisenberg started avoided quantum field theory, when Dirac started avoided renormalization, physicists thought that they were misguided and moved on ignoring them.
Now, page 2 of the short paper starts: «Let X be a Kahler manifold, and W : X → C a holomorphic Morse function. To this data physicists associate a “Landau-Ginzburg model.” It is closely related to the Fukaya-Seidel (FS) category» and concludes «Two of the motivations for the detailed construction of interfaces are the nonabelianization map of Hitchin systems that arises in theories of class S, and the application of supersymmetric gauge theory to knot homology».
Seriously: I don’t know what to think about this. Do such two-dimensional SUSY systems have relevance for physics? If yes, how? Or are they a way of avoiding physics?
Hi Peter,
Thanks, I got it.