Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Grisha got it!

  1. Aug 22, 2006 #1

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Grigori Perelman was awarded the Fields
    the other three Fields winners are Tao, Okounkov, Werner

    http://icm2006.org/v_f/web_fr.php?PagIni=1pl

    looks like he will not be giving an acceptance talk, only three of those.
    but his is the second Laudation talk

    ==============
    when you go to the official ICM 2006 site, at that link, click on "prizes" in
    the lefthand sidebar menu

    you will see that there are 4 "Laudatio" talks for the 4 Fields winners
    Perelman, Tao, Werner, and Okounkov

    this I take to be a clear indication that one of the four medals has been awarded to Grigori Perelman
    anybody have some other explanation?
     
    Last edited: Aug 22, 2006
  2. jcsd
  3. Aug 22, 2006 #2

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    I believe he actually declined the medal.
     
  4. Aug 22, 2006 #3

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    apparently at one point he DID decline the medal
    and as of last week it looked like he at least would decline to go to Madrid to accept it

    but why do you think NOW that he is not getting the Fields?
    do you have any recent news to tell us?

    ====EDIT====

    WOW it looks like you are right!
    Neutrino points me here:
    http://rawstory.com/news/2006/2ND_Russian_becomes_first_to_reject_08222006.html

    I thought he had not finally rejected but had changed his mind and would accept.
     
    Last edited: Aug 22, 2006
  5. Aug 22, 2006 #4

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    Look at this press release
    http://www.icm2006.org/press/releases/

    http://www.icm2006.org/dailynews/fields_perelman_info_en.pdf

    ===quote===
    INFORMATION EMBARGOED UNTIL TUESDAY AUGUST 22ND, 12:00 AM, CENTRAL EUROPEAN TIME) Fields Medal Grigory Perelman CITATION: "For his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow" The name of Grigory Perelman is practically a household word among the scientifically interested public. His work from 2002-2003 brought groundbreaking insights into the study of evolution equations and their singularities. Most significantly, his results provide a way of resolving two outstanding problems in topology: the Poincare Conjecture and the Thurston Geometrization Conjecture. As of the summer of 2006, the mathematical community is still in the process of checking his work to ensure that it is entirely correct and that the conjectures have been proved. After more than three years of intense scrutiny, top experts have encountered no serious problems in the work. For decades the Poincaré Conjecture has been considered one of the most important problems in mathematics. ...
    ===endquote===
     
  6. Aug 22, 2006 #5
  7. Aug 22, 2006 #6

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

  8. Aug 22, 2006 #7
    "In 1996, Perelman refused a prize from the European Mathematics Society on the grounds that the jury was not qualified to judge his work."

    Hehe, that may actually be true.
     
  9. Aug 22, 2006 #8
    Now, all that's left are a book by Akiva Goldsman and a movie by Ron Howard. I will definitely want both to be titled Grisha. :biggrin: No, wait, those can't be of the slightest public interest. :tongue:
     
  10. Aug 22, 2006 #9

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    After all the Grisha fuss, did you check out the talk by Terence Tao? Fascinating! Although the primes are such a scrawny subset of the integers, yet they contain arbitrarily long arithmetic sequences (i.e you start on a prime somewhere and add a constant and keep adding, and all the numbers you hit up to some end point are primes. And the distance to the end point can be chosen as big as you like. As Tao says, it shows us how order and randomness nestle together!
     
  11. Aug 22, 2006 #10

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    one of my friends and colleagues, valery alexeev, is an invited speaker in madrid, and he is emailing us news as it happens.
     
  12. Aug 22, 2006 #11

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    i want to specifically advertise the talk by my friend valery tomorrow, in the complex algebraic geometry session. his work is extremely interesting too, on classification of abelian varieties, and moduli of "stable pairs".

    valery has completed the program of compactifying moduli spaces of abelian varieties, begun by riemann and continued by many, including mumford, mori, namikawa, baily, borel, etc..\


    his most recent work suggests a higher dimensional analog of the work of mayer, mumford, deligne, kontsevich, oncompactifying curves by "stable curves", which led to quantum cohomology and the work of witten. (We heard a preview last week of valery's talk scheduled for tomorrow.)
     
    Last edited: Aug 22, 2006
  13. Aug 22, 2006 #12

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    neutrino, maybe it would sell better if it were titled "take this prize and shove it", with a country western theme.
     
  14. Aug 23, 2006 #13
    Am I the only one more interested in Tao's achievement than Perelman's?
     
  15. Aug 23, 2006 #14

    George Jones

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    selfAdjoint beat to to it; see post #9 in this thread.
     
  16. Aug 23, 2006 #15

    Astronuc

    User Avatar
    Staff Emeritus
    Science Advisor

  17. Aug 23, 2006 #16

    marcus

    User Avatar
    Science Advisor
    Gold Member
    Dearly Missed

    the story in the New Yorker is now available

    http://www.newyorker.com/fact/content/articles/060828fa_fact2

    it is written by Sylvia Nasar, the author of "A Beautiful Mind" about the mathematician Nash.

    she was already in St Petersburg in June this year, researching it, and she is a good writer, so it might be interesting and different
     
  18. Aug 23, 2006 #17
    ha ha...I just realised my mistake in my last post. I actually meant Sylvia Nasar, and not Akiva Goldsman.
     
  19. Aug 23, 2006 #18

    mathwonk

    User Avatar
    Science Advisor
    Homework Helper

    thats very impressive, but not to me as impressive as the poincare conjecture, or its solution.
     
  20. Aug 28, 2006 #19

    gvk

    User Avatar

    I want to understand why 3D case is totaly different from 1D-2D and nD,
    n > 3 for which analoques of Poincare conjecture were proof a long time ago. Why the dimention 3D is really matter?
     
  21. Aug 28, 2006 #20
    That question's been nagging my mind, too. I'm don't know about gvk, but I'm a complete outsider to pure maths. So all you math-types, keep your explanations simple. :biggrin:
     
  22. Aug 28, 2006 #21
    Supposedly, in 3d there isn't enough dimensions (only 3) to do their math stuff. Where as in higher dimensions you can utilize alot of different techniques because you have lots of room to move around.
     
  23. Aug 28, 2006 #22

    selfAdjoint

    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed


    You got it. The one and two dimensional cases are trivial, and the n greater than three results, while difficult, were solved by Smale a long time ago. The reason three-manifolds are so interesting is that they are right on this boundary between being so limited they're trivial and being so unlimited they're trivial in a different way.

    Back when I was a beginning topology student I was not very interested in three-manifolds (which had been an active subtopic since Poincare's day), thinking, "Well then, when they get that all resolved they'll just have to go on to four-manifolds, and then 5, 6, ..., google, ...". It seemed like a mug's game to me. But it ain't so; three is, even at the most abstract level, a very special, very important case.
     
  24. Aug 28, 2006 #23

    gvk

    User Avatar

    Thanks, selfAjoint.
    Now, more specific question: if the Ricci-flow technic works just fine for 3D case (on the boundary), it can work for nD case (n>3). Is that correct?
    And what does mean the parameter t in Ricci-flow eq.: d (g_{i,j})/dt =-2*Rici? My guess: we issue any parametric curve on manifold from point P and take derivitive along it. Correct?
    Sorry, I don't have any original Hamilton paper to look details.
     
  25. Aug 29, 2006 #24
    Actually, the "t" is the variable for a parametrized curve of metrics on the manifold. I.e. for each fixed t, g_t is a Riemannian metric over the entire manifold.

    In other words, they are looking at the (infinite-dimensional) space of all Riemannian metrics living on the given 3-manifold and studying paths in that space that satisfy the Ricci-flow equation, which is actually just a differential equation.


    Regarding the strangeness of 3- versus higher-dimensions, dimensions 3 and 4 seem to be -- in general -- harder to work with than higher dimensions. 4-manifold theory is quite active these days, although it got a little "easier" when the Seiberg-Witten equations were discovered in the early 90s.
     
  26. Aug 30, 2006 #25

    gvk

    User Avatar

    Thanks, Doodle Bob.
    It seems that the application of Ricci-Flow equation to the dimentions n>3 is not straightforward because Riemann curvature for n>3 is not totaly defined by Ricci tensor, which is the right side of Ricci-Flow equation. Is that correct?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook