If you just can’t get enough of pictures of mathematicians, head over to the Oberwolfach Photo Collection. This is a huge collection, which I recently ran across when trying to locate something by Graeme Segal. It also includes a photo of a frequent contributor here.
The AMS has put quite a few whole books on-line. Recently they added the three-volume set A Century of Mathematics in America here, here, and here. Another interesting volume is Mathematics into the Twenty-First Century, which includes some wonderful survey articles, including a very long series on Lie theory by Roger Howe, and one on Geometry and Quantum Field Theory by Witten.
Terrance Tao has a sort of research blog.
In the category of interesting-looking work that I haven’t yet had time to read carefully and think about, here are two papers on an approach to studying pure Yang-Mills theory, by Freidel and Freidel and collaborators.
Update: A correspondent suggests I mention another famous mathematician whose photo is on the Oberwolfach site.
Speaking of Ted Kaczynski, anybody have a clue as to why he left math in the first place? (Of all the articles and books I’ve read about him over the years, I haven’t been able to find an explicit reason as to why he left math).
If I had to guess, maybe Ted got bored of math?
Great stuff!
There’s been some legitimate and constructive criticism of the recent work on 2+1d YM. Some people, whom I consider experts in “ordinary” QCD — including but not limited to the authors of recent Pomeron research –, have raised some questions that ought to be answered before relying on those results as a starting point for new research.
JC: according to Wikipedia, he just wanted to live as a hermit – which is not a bad idea after all.
And he was preparing his anti-technological revolution.
I did not know this guy until 30 minutes ago. Interesting. A few minutes ago, I just tried to solve the quiz “Gore or Kaczynski”
http://www.crm114.com/algore/quiz.html
and got exactly 50 percent of the answers right, which is exactly what one gets by guessing. Can you do better?
Although I have some compassion and understanding for Unabomber, it is rather clear that our colleague Bill Cottrell probably has much more understanding. 😉
Ted Kaczynski is a hero, a man of honor and courage.
Ted Kaczynski is also a true freedom fighter.
I’m sure you said that with a very straight face jay. 😉
lubos, some of Ted Kaczynski’s ideas may seem to similar to that of Al Gore’s, but they are really quiet different. You should read his manifesto at http://www.thecourier.com/manifest.htm
Tao’s habit of commenting each new paper is nice and I hope it will generalize (I know a few other interesting examples), instead of just putting a kind of in-your-face dense list of papers.
The latter may impress grant-related committees, but it’s of little use for the would-be grad student, and for colleagues as well…
‘… according to Wikipedia, he just wanted to live as a hermit – which is not a bad idea after all.
‘And he was preparing his anti-technological revolution.’ – Lubos Motl
Dear Lubos,
have you any plans to follow in Kaczynski’s footsteps?
🙂
Dear knotted string,
I happen to have the opposite opinions about technology than Kaczynski, and if I am tempted to send someone mail bomb, it’s the people who say that the technological progress destroys the ecosystem – people like Al Gore. I say Al Gore instead of Unabomber because Unabomber is already arrested which is OK with me.
Let me emphasize that I have no short term or long term plans to send mail bombs. 😉
Dear jayhod, Kaczynski was almost certainly a more courageous character than Al Gore, but let me stay away from the fan clubs of both of these Gentlemen if it’s OK with you.
All the best
Lubos
Just for the record (since Lubos is a bit vague about this), Billy Cottrell was a vandal, not a murderer. He does not deserve to be compared with the likes of Kaczynski.
Dear A.J.,
no doubt that there is a difference but you can see that even Kaczynski has his own admirers here. 😉
All the best
Lubos
Witten is not in the photo collection. Having a Fields Medal is not enough to get oneself into the collection, I guess.
Al Gore is not really anti-technology, after all, he’s on the board of Apple Computers. Al Gore’s a pro-technology green. Ted Kaczynski’s criticism of technology is not limited to its effect on nature, but also its effects on human, for example he disliked genetic engineering because it’s potential to change what it means to be human. Ted Kaczynski’s a neo-luddite.
has anybody read the paper by Freidel Minic and Leigh that Peter linked to in the initial post?
Try Thoreau or Kaszinski instead
Try Thoreau or Kaszinski instead
Sorry to be grouchy, Eli. BTW I liked your translation of the article in Die Zeit.
there’s all kinds of atavism in the world—lots of ways to be luddy-minded—some trash technology and some sabotage their own or their neighbor’s mental faculties
I want to know by how far Freidel missed the Clay million.
Why is Freidel the only one you’re mentioning? This is just an attempt to extend the interesting work of Leigh, Minic, and Yelnikov in the 2+1 dimensional case, which is in turn an outgrowth of work by Karabali and Nair. But of course readers of this blog seize on the one person who has worked on “alternative” approaches to quantum gravity as the person to mention and ignore the contributions of others. In any case, it is clearly not yet very close to being what the Clay Institute wants.
thanks, why is it not yet close? what remains to do (if not too much bother to summarize briefly)?
Let’s call it the work of Minic Leigh and Freidel, simply changing to reverse alphabetic order.
The interest from a quantum gravity viewpoint is that there are some papers by F. and Sean Majid, by Baratin and F., and by F. and Livine that get some results in 2+1 dimensions certain parts of which are said to be extendable to 3+1: a problem being presently addressed. there may be some common element in how they try jacking up the dimension in both cases from 3d to 4. I don’t know that there is, but the possibility seemed there.
anonymous,
The reason for mentioning it has nothing to do with Freidel’s work on quantum gravity and everything to do with the fact that it’s in 3+1, not 2+1 dimensions. The Karabali + Nair and later work in 2+1 d is quite interesting, but 3+1 d is very different and personally I was always dubious that you could do anything in 3+1 d with their methods. If Freidel and collaborators actually can, that will be very exciting. I just haven’t had the time to read their papers carefully enough to see exactly how far they’ve managed to get. Like Who, I’d be interested to hear from someone who has carefully read and understood these papers (but not interested in hearing from people whose reaction is just to dismiss Freidel’s work because he also works on an alternative to string theory).
Well, we’re more or less in agreement: (3+1)d is indeed very different, and it would in fact be very exciting if a result is achieved. Here’s my understanding of the current status.
One defines a set of variables as follows. For a given point “x”, one takes Wilson lines extending along one of the axes from infinity in to x, and then along a different axis from x out to infinity. This provides a set of local, gauge-invariant operators. They have some nice properties related to holomorphy in 2D, and in 3D they satisfy some identity H_{ij}H_{jk}H_{ki}=1 (and can also be formulated in a somewhat holomorphic way).
Next one shows that there is a nice Hamiltonian approach to studying the theory in terms of these operators and some associated currents. There are some subtleties about regularizing in the right way but they seem to have addressed these.
The next problem is to construct the vacuum wave functional. In (2+1)d there turned out to be a simple analytic solution in the large N limit. In (3+1)d, it is not nearly so simple, and they seem to have currently only some wishful thinking. In the UV they find that a free-field ansatz seems to work (it had better!), and in the IR something with a mass scale might work. But the detailed form of the solution is completely mysterious.
Unfortunately, that mass scale is just added by hand (effectively, it’s a cutoff) and so far there is no connection of UV to IR in which we can see that it really is the QCD scale and is related to logarithmic running. They hope to find some self-consistent solution showing there really is a nonzero mass. To do this would certainly be a major breakthrough, and I hope it can be done, but it hasn’t yet.
If all of this works it’s at best a solution at large N, but that would still be very exciting. However, the current status reminds me of some old work of Migdal on solving the loop equations; there are tantalizing hints that there is something deep there, but no one ever seemed to know quite what to do with it. (In fact, you might think of this more recent approach as working with a subset of the loop variables, namely those loops that go through the “point at infinity” and remain parallel to one of the axes at all times.)
To Peter and anonymous:
with all caution I would like to take the following optimistic view on the Freidel et al work.
It should be viewed as being connected with Stanley Mandelstam’s old program (Ann. of Phys. 19 (1962)) of substituting gauge theory by a formulation in terms of field strength. This old idea has received a significant conceptual underpinning through our recent work on semiinfinite spacelike string-localization derived within the new powerful setting (Mund, Schroer, Yngvason in print in CMP, math-ph/0511042) of modular localization. In that setting the family of massless finite helicity=s Wigner representations have pointlike field strength but (in the same Hilbert space, hence no ghosts!) covariant semiinfinite spacelike localization. As a result the the associated quantum potentials A(x,e) fluctuate in both the Minkowski space x and the De Sitter e (unit spacelike string direction) which leads to an improved short distance behavior (scaling dimension 1 independent of s). These objects are not Lagrangian fields but the properly adjusted (to strings instead of pointlike fields) Epstein-Glaser approach seems to work. For s=1 the string-independent subalgebra corresponds to the gauge invariant observables. But for s=2 (Gravitation, dimg(metric potential)=1) this is virgin territory since there does not seem to exist any gauge setting in terms of unphysical pointlike potentials. If the calculations continue to live up to our expectations we should have in due time a “renormalizable” setting for gravitation (where renormalizable means that from an infinite parametric universal Bogoliuvov-Shorkov-Epstein-Glaser matrix S(couplings) we are able to filter out a finite parametric set). This together with the strong arguments bu Brunetti and Fredenhagen that the perturbation can be arranged in such a way that (using their quantum local covariance principle) that a perturbative version of background independence results.
Maybe I project too much into Freidel et al ideas, as with any computational work whose conceptual basis is yet nebulous I may have taken an overly optimistic interpretation.
Woudn’t it be ironic if string-localization (not at all related to string theory) achieves what string theory promised?
Question to Peter: suppose what I described can be in due time converted into hard facts, what would you thing string theorists will do if they loose their only supporting argument?
small correction to an important statement in my text
“In that setting the family of massless finite helicity=s Wigner representations have pointlike field strength but (in the same Hilbert space, hence no ghosts!) covariant semiinfinite spacelike” localized potentials.
anonymous,
Thanks for the very informative comments on the Freidel et.al. work!
Bert,
If the scenario you describe pans out, string theorists will announce that it is part of “string theory”, closely related to what they had in mind all along, and proclaim victory.
What a coincidence, given their hegemonic all-devouring sociological situation this is precisely what I also expected!
In this case the word “string-localized” would make it quite easy for them (the fact that its conceptual meaning is lightyears apart from string theory would be no obstacle for people who live in a conceptual twilight zone).
Don’t forget the pony.
Great idea Aaron, let’s add “and a pony” to all string theory papers coming out these days. Would be highly appropriate…
Just the ones that don’t calculate anything.
What % is that?
Since 0% of string theory papers calculate anything that can be compared to the real world, I guess he means ones that calculate something, with the hope that someday it will lead to some calculation that can be compared to the real world. These papers deserve “and a pony” as much (and often, more) than any others.
The least you can do when you don’t have any hope of comparing with the real world is to calculate something. Otherwise you get “wouldn’t it be nice if…” papers. Wouldn’t it be nice if we all had a pony?
Just doing random, pointless calculations doesn’t make you a scientist. If you want to claim that your calculation is part of science, you have to be able to show that it has some hope of being related to the real world. Right now, just about all string theory calculations are motivated by “wouldn’t it be nice if” hopes. Some of them very bizarre, e.g. “wouldn’t it be nice if the world were some random point in some horrifically complicated space and we could never predict anything…”
I enjoyed browsing through the pix, but they’re not well catalogued. There’s an entry for Marsden, Jerry and for Marsden, Jerrold E. ; Singer, I. and Singer, Isadore. Several photos are only labeled by last name. One I am curious about was “Love”, it isn’t me (of course) and it’s too recent to be AEH Love.
We all know you dislike string theory, Peter.
One reason being that string theorists, lacking any real arguments, can’t stop themselves from descending to ad hominem ones
You could perhaps enjoy messages 16, 28 and 29 in this thread:
http://www.physicsforums.com/showthread.php?t=120192&page=2
one can use math a lot simpler than string theoretists and still come to results of fuzzy and membranous interpretation.
I glad you kept that in such general terms because I haven’t made any ad hominem remarks in this comment thread. Nonetheless, as enjoyable as this exchange has been, I’ll bow out now unless something new happens to come up.
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