Wednesday, March 20, 2013

Pierre Deligne wins Abel Prize

Viscount Pierre Deligne of Belgium won the $1 million Abel Prize, a major award given to mathematicians, today. It's a well-deserved honor, I think.

He is perhaps most famous for the proof of several Weil conjectures, (now) theorems about various Riemann zeta functions and related facts generalized to the case of finite fields. This is enough to see that Deligne is primarily an algebraic geometer, in the tradition of Alexander Grothendieck.

However, the depth of a mathematician may arguably be measured by the extent to which his or her insights start to influence cutting-edge theoretical physics in the present and, if possible, in the future. For decades, this criterion was equivalent to the role that the mathematical insights play in string theory. Deligne gets an A in this subject, too.

First of all, he has made quite some work on the Hodge theory which is concerned with differential forms on manifolds and its role in string theory is self-evident. However, this is a sort of trivially stringy part of Deligne's research. There is a more abstract example that shows that some research by Deligne is very close to some principles that certain string theorists may consider central yet heavily underappreciated.

What am I talking about?

Well, I mean the algebraic stacks – Deligne-Mumford stacks and their generalizations, Artin stacks. They were originally introduced to describe the fine moduli space of genus \(g\) curves (Riemann surfaces) and as algebraic counterparts of orbifolds. The links to string theory world sheets and stringy orbifolds is obvious.

However, there's much more stuff beyond these structures that isn't obvious but may be important for string theory. Imagine that this portion of the blog entry contains an insightful lecture on stacks, sheaves, derived categories, and their ability to classify everything that may be included into the most generalized notion of D-branes. Apologies: I will omit it because it wouldn't satisfy the quality standards I demand here.

Shamefully enough, Deligne's textbook of field theory and string theory for mathematicians has never been mentioned on this blog. So at least, I am trying to undo the grievance right now. To a large extent, it is a rather standard physics textbook. Nevertheless, it may be interesting for a physicist to listen to the "accent" that a top mathematician displays when he talks about similar issues.


  1. Wow! What a guy. Deligne’s work shows me how very little I know; he is obviously a master of his craft.
    The photo of Deligne has to be another Lubos job. It’s just terrific.

  2. LOL, thanks a lot but I didn't take the photo although it's a similar style to some photos I did take. ;-)

  3. Cool guy and congratulations to him !

    "However, the depth of a mathematician may arguably be measured by the
    extent to which his or her insights start to influence cutting-edge
    theoretical physics in the present and, if possible, in the future."

    Yep, this makes me LOL in heartily agreement :-D

  4. Slightly off topic:

    Concerning another valuable prize, it seems Alexander Polyakov will catch a huge buck of money very soon and rightly so:

    Cheers :-D

  5. You said "the depth of a mathematician may arguably be measured by the extent to which his or her insights start to influence cutting-edge theoretical physics"

    Oh FFS Lubos. I say this in friendship but... please, don't make me argue about this, because I am your fan. This reminds me of your assurance that 1+2+3+4+5+... = -1/12. What is wrong with physicists? God damn it. If you're so fucking great then prove the Riemann hypothesis. Jesus Fucking Christ. I remember one post where you claimed that physicists are smarter than mathematicians. Bullshit. OK I've said my piece.

  6. Well then please don't do any math. It would be like handing a razor to a baby in the bathtub.

  7. are you on medication? give actual arguments.

  8. Your head is apparently stuck up your ass, faggot (not that there's anything wrong with that), but may I point out that 1+2+3+... diverges?

  9. Only if you know totally elementary math, Jason. Euler (a mathematician, in case you were unaware) proved that it equals -1/12 and didn't really know what that meant. Riemann did (another mathematican). The regularized Riemann zeta function is just that infinite series with zeta (-1) and that works out to -1/12.

    This occurs in bosonic strings---calculating the energy of all the harmonic oscillators from the fundamental is adding nh(bar)omega/2 for n natural numbers to infinity and that equals -h(bar)omega/24 ie -1/12 times h(bar)omega/2.

    Why not try being less of an a$$h@le and learn something.

  10. Hmmm, seems you agree with Barbie-"Math is hard..."

  11. Gordon, no. On this very blog I have suggested that Zeta(-1) = -1/12 is the correct formulation. I have a PhD in math.

  12. Barbie is correct, math is hard, indeed harder than physics.

  13. That would be great although it's true for some competitors such as Polchinski, too.

    I find Matt's explanation of Polyakov's key contributions highly tendentious as it completely ignores the three papers that Polyakov wrote and that are by far most influential in his list.

    One is the 1998 understanding of correlators in AdS/CFT with Gubser and Klebanov, 6,000 cits.

    The other one, with 4,000 cits, is his, Belavin, and Zamolodchikov's 1984 understanding of infinite conformal symmetries in 2-dimensional CFT. All the mathematical structure with inner products of states interpreted via the state-operator correspondence and similar matters came from BPZ.

    The third most influential paper was written by Polyakov himself and it has nearly 3,000 cits: it's the BRST treatment of the bosonic string from 1981 that became the preferred method to calculate any string theory of all the new string theorists who joined in the mid 1990s.

    Strassler's ignoring of these 3 key things suggests that his censorship wants to compete with that of North Korea.

  14. I think Lubos needs to intervene here.

  15. Here is a proof if you want one and are not just trolling:

    If you are just trolling, please F.O.

  16. Then why are you dissing Lubos for posting this? Euler submitted a proof of sorts before the zeta fn was properly defined by Riemann. As far as who is smarter, I think it is often a tie and some are both, like Witten and Penrose, Freeman Dyson, to some degree Atiyah, Connes. Also, there are stupid ones in both. They view things somewhat differently. Mathematicians are obsessed with proofs. Physicists, with discovering laws of nature often arising from mathematical structures. But this is a trivial observation. I would argue that the best in each discipline are quite equivalent---look at Newton and Leibniz---mathematicians or physicists? The Bernoullis? Huygens? Poincare?

  17. Barbie rules!

  18. Dear Lumo,

    hm, when reading the corresponding title on Matt Strassler's site for the first time and realizing what the post is about, I was prepared to read a rant from him against Mr. Milner corrupting science, Polyakov accepting the prize, etc ... so it was not that bad as I personally thought first.

    However, I noticed too that Matt Strassler tried to highlight Polyakov's early QFT achievements and sweep his stringy work rather under the rug ... ;-).

    But even the fact that he dared to mention string theory in a positive definite non negative manner, was enough to attract trolls of the worst kind, have you seen the first comment ... :-/ ?

    I bet soon the comment section will become unreadable for serious people who like physics ...

    I really wonder why he does not throw the trolls out but instead tolerates that Michio Kaku, Gordon Kane, and other physicists get badly insulted on his site by scum ...

    To look on the bright site of life, I look forward to reading the article you have read about the new FPP winner :-).

    Since I have seen that it oviously contains nice detailled physics explanations to it will have to wait till I'm at home, such that I can properly enjoy and devote enough time to this article.

    But thanks in advance :-D


  19. Oh dear Jason,

    I think there is no need for you to get upset too much ;-)

    As I interpret it, Lumo wanted by this sentence just to tease his mathematician readers a little bit (in a much friendlier way than what did this Tyson guy with Brian Greene) without meaning any harm or disrespect to mathematics or the people doing research in this field.

    I just see it as one of his joking comments (that do not have to be taken too seriously) he often puts into his articles and that is why it made me LOL.

    You probably know Lumo better than I do, but from reading what he says here on TRF and elsewhere I got the impression that he highly appreciates mathematicians and the beauty or cuteness of their field on its own too ...

    And so do I as far as I am knowledgable enough to see it ...:-/

    For example I was highly impressed by what nice progress can result in both, mathematics and physics, when people in both fields help and inspire each other as described for example in

    "The Shape of Inner Space"

    So please, dear mathematicians and physicists be nice to each other :-)


  20. ...depends on what you mean by "math" and "physics"--like Clinton's "It depends on what the meaning of "is" is." It is enormously hard having the physical insight into reality to recognize and use mathematics to model nature.
    Sure, math can be as easy or difficult as you imagine. And some physics can be as easy as observing something. Often the difficulty in math is providing a rigorous proof. Most physicists have a "good enough" attitude if the correspondence with nature is strong.

  21. Hands and eyes are helpful for brain just like physics and math for scientific knowledge or fire and ligth for humankind (I am pretty sure), big mouth and highbrow are dispensable (I guess) ...