ICM 2006 Fields Winners: Perelman, Tao, Okounkov, Werner Laudatio Talks

[marcus]

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?

 

[mathwonk]

I believe he actually declined the medal.

 

[marcus]

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.

 

[marcus]

I believe he actually declined the medal.

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

22 August 2006 "Information about Grigori Perelman, Fields Medal winner"

22 August 2006 "Picture of G. Perelman"

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===

 

[neutrino]

Yes, he has declined the prize.
http://www.math.columbia.edu/~woit/wordpress/?p=448

Check out the link from in Jeremy in the comments.

 

[marcus]

good grief!
Jeremy's pointer is to this
http://rawstory.com/news/2006/2ND_Russian_becomes_first_to_reject_08222006.html

 

[waht]

"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.

 

[neutrino]

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. No, wait, those can't be of the slightest public interest. :tongue:

 

[selfAdjoint]

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!

 

[mathwonk]

one of my friends and colleagues, valery alexeev, is an invited speaker in madrid, and he is emailing us news as it happens.

 

[mathwonk]

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.)

 

[mathwonk]

neutrino, maybe it would sell better if it were titled "take this prize and shove it", with a country western theme.

 

[DeadWolfe]

Am I the only one more interested in Tao's achievement than Perelman's?

 

[George Jones]

Am I the only one more interested in Tao's achievement than Perelman's?

selfAdjoint beat to to it; see post #9 in this thread.

 

[Astronuc]

For those just joining . . .

http://en.wikipedia.org/wiki/Terence_Tao

Pretty impressive!

http://www.math.ucla.edu/~tao/

 

[marcus]

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

 

[neutrino]

ha ha...I just realized my mistake in my last post. I actually meant Sylvia Nasar, and not Akiva Goldsman.

 

[mathwonk]

thats very impressive, but not to me as impressive as the poincare conjecture, or its solution.

 

[gvk]

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?

 

[neutrino]

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?

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.

 

[waht]

Supposedly, in 3d there isn't enough dimensions (only 3) to do their math stuff. Where as in higher dimensions you can utilize a lot of different techniques because you have lots of room to move around.

 

[selfAdjoint]

Supposedly, in 3d there isn't enough dimensions (only 3) to do their math stuff. Where as in higher dimensions you can utilize a lot of different techniques because you have lots of room to move around.

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.

 

[gvk]

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.

 

[Doodle Bob]

TAnd 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?

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.

 

[gvk]

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?

 

[mathwonk]

the two dimensional case follows from a clasification of all 2 manifolds S OBTAINED BY joining handles to spheres. the three dimensional case wouldfollow aND APPRENTLY DOES, FROM AN analogous conjecture of thurston on how to obtain three manifolds from joining various basic types of objects.

the definition of "trivial" is of cousre open to discussion, but m,y definition is nythign I MYSELF KNOW HOW TO DO, AND I CANNOT SAY I NKOWHOW TO PROVE THE CLKASIFICATION OF 2 MANIFOLDS.

help! i should have taken typing asa high school studentbut in thsio days it was only offered to secretaries!@

 

[mathwonk]

recalling my ancient history courses in 2 manifolds, i seem to recall that clasificaion of 2 manifolds is ropecedded by a proof that all 2 manifolds are triangulable, itself perhaps not so easy.

or maybe there is an easier morse theory proof?

 

[gvk]

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.

The full answers to such trivia questions are available now in references here:
http://en.wikipedia.org/wiki/Grigori_Perelman

 

[J77]

A very impressive CV, that Tao guy's got.

It's amazing when you see people your own age with results like that!