The International Congress of Mathematicians is held every four years, and the next iteration, ICM 2010, will be held about a year from now, in Hyderabad, India. These are huge conferences, planned well in advance, with 1465 mathematicians already pre-registered.

The list of speakers gives a good indication of what the mathematical establishment views as the most important research activity of the past four years, and this list is now available here. There are a large number of parallel sessions, and a limited number (20) of plenary talks.

The winners of the Fields medal are announced at the ICM, at the same time as the composition of the committee that made the choice (the chair of the committee, Laszlo Lovasz, is known). One way to help guess who will win a Fields medal is to take a look at those on the speakers list who are under forty. I’m not privy to any inside information, but many people think Ngo is a shoo-in for his work on the fundamental lemma (he’s a plenary speaker), and there’s some speculation about Jacob Lurie (who is a parallel session speaker).

This year there’s a new prize to be awarded at the ICM, the Chern Medal, for “an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics.” This one, unlike the Fields, comes with a significant amount of money ($250,000, and another $250,000 for the medalists favorite mathematical organization).

“there’s some speculation about Jacob Lurie”

What has we done?

Regarding the Chern Medal, is it for people <40 years old as the Fields Medal?

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I see Matilde Marcolli is one of around ten invited speakers in the Mathematical Physics section.

She just posted http://arxiv.org/abs/0908.3683

Early Universe models from Noncommutative Geometry

In the ICM list of plenary speakers why there is “USA” for Ngo Bao Chau?

He is vietnamese and studied in France under Gerard Laumon : http://en.wikipedia.org/wiki/Ngo_Bao_Chau

egan,

I believe Ngo is now at the IAS in Princeton.

Manel,

The Chern Medal has no age restriction.

For Lurie’s work, see his home page, or search the n-category cafe or secret blogging seminar for blog entries about this.

Thanks Peter.

PS: I obviously intended to write “What has

hedone?”Actually, 4 years ago the math blogosphere wasn’t as developped as it is today, so let’s hope the gossiping still remains minimal.

Yet, since I’m no insider, and since your post is an invitation for gossiping let me venture an opinion, namely that I’m not surprised to see Avila getting a plenary, he has the typical Field medalist pedigree (PhD aged 21, still only 30 today, many major papers and large output, former IMO gold medalist… ticks all the boxes).

Avila…

>>>I believe Ngo is now at the IAS in Princeton

Peter,

So what ? Ngo is vietnamese and not american.

If you look at the ICM speaker list for Artur Avila you will see he is brazilian. He work in Paris but near his name on the ICM list there is “Brazil” and not “France”.

Near Ngo’s name it should be “Vietnam” and not “USA”.

egan,

Avila’s CV has him with a French CNRS position, but now on leave from Paris and affiliated with IMPA in Rio. The countries listed seem to be not citizenship but location of current academic affiliation.

Irit Dinur looks like a shoe-in for the Nevanlinna (she’s under 40, right? she certainly looks it…) although it’d be fantastic if she won the Fields. (Why do I say this? Because she’s a plenary speaker without the status of a Goldwasser or a Wigderson, and her work on PCP certainly qualifies her for a Nevanlinna. It’s possible that Aharanov could get it, though, although I’m less certain that she’s under 40.)

Manjul Bhargava is conspicuously absent from the speakers list, although I’m pretty sure he has another cycle of eligibility. Chandrashekhar Khare was born in 1968, and is ineligible. Avila has two more cycles of eligibility, and most of the time the Fields committee tends to wait in such cases. (Think of Deligne; think of Drinfeld, who could have won in ’82, ’86 or maybe even ’78 without anyone batting an eye.) Lurie also has two more cycles. I think by far the best bet is on Ngo, with Avila strongly in the running.

Yes, there are many deserving candidates obviously, so indeed it may ultimately push things more and more towards recipients in their late thirties, with twenty-something winners not occuring anymore.

Looking at the list of speakers a little more and crossing it with winners of prizes like European Math Soc. and Salem, it looks like Assaf Naor especially is another strong young contender, at least for future cycles.

Kisin?

Manjul Bhargava, Ben Green, Cedric Villani and Bao Chau Ngo.

cedric villani or alexander kuznetsov

Christopher Hacon..

(Lurie and Venkatesh in 2014?)

I think they’d wait for Lurie… his work still is unpublished and he’s well under 40. Avila is a good candidate although young himself.

I’ve heard rumors about Kiran Kedlaya from MIT. And sure enough, he’s an invited speaker in the number theory session.

Slightly related, any news about Grigori Perelman lately?

chickenbreeder,

I haven’t heard anything at all about Perelman recently. There the interesting question is what Clay is going to do about the million bucks for the proof of the Poincare conjecture.

yun zhiwei

yuan xinyi

Look at the papers of Kiran Kedlaya, given that Laszlo Lovasz is the chair he would be my best bet with Bao Chau Ngo who is a certainty

I guess all those Clay Math scholars and award winners are all potential candidates. Don’t you think it would be interesting to have a first female Fields Medal winner in the history of math? The third winner’s name may not have been heard of by us in the US.

As you can see from the list of speakers in each field, there are many new names. But the ultimate question goes to “what has he or she done so significant?”

If for age priority, the chance that Venkatesh and Rodnianski are also good candidates. But you will never know. Ngo is the only certainty.

By the way, Who would be the candidates for Chern Medal? Serre?

I don’t think there are any certainties in the fields medal this time around. Last time there was Perelman who was pretty certain, Tao was pretty certain to get one eventually, but I don’t see now anyone standing head and shoulders above the rest… I guess we’ll have to just wait and speculate

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I was under the impression that the Fields was given to people who solved big or hard problems. So, that rules out some of the people listed, right?

I was under the impression that the Fields was given to people who solved big or hard problems. So, that rules out some of the people listed, right?It’s hard to say. The committee has a lot of discretion, and there’s no clear cut-off for what constitutes a “big or hard problem”. Some of the people mentioned here seem an awful lot more likely to me than others, but that’s what you’d expect from blog comments, and there’s enough unpredictability that I wouldn’t bet my life savings against the less likely candidates.

With regard to hard problems, it is useful to recall the old joke : Thurston proved that you could win a Fields medal without ever writing out a proof, but then Witten proved that you could win one without even stating a theorem!

That said, Ngo is the only person I feel at all confident about.

Bao Chau Ngo, is working on Langlands and solved some important issues, and that was probably a reason why he was brought to the IAS. Avila could be a deserving choice too. As athird choice I think Jacob Lurie could be in the run.

If you ask me: As Richard Schoen is a plenary speaker, in my opinion Simon Brendle from Stanford is a good guess for the fields medal. As far as I know he is not even 30 years old.

Simon Brendle is a great mathematician. But they have given it last time to Perelman (in differential geometry/geometric analysis). So it may not be likely to give the Prize to mathematicians who are in the same field again unless they have some astonishing breakthrough comparable to the resolution of Poincare Conjecture. Brendle’s works are excellent but he’s got many competitors in the field. He has a chance though, but maybe not this time.

For the field of Number Theory, it’s competition is even more intense: Bhargava, Venkatesh, Soundararajan, Mark Kisin, Ben Green, etc. As Lovasz in the chair position, Sudakov is a good candidate for combinatorics (though not sure if he’s still under 40 by the time). For Algebraic Geometry, there are many competitors as well: Christopher Hacon, Jacob Lurie,

I think all those who are Clay, AMS, AIM, or EMS Award Recipients under 40 are stronger candidates. Reading the ClayMath winners, Rodnianski, Ian Agol and D. Calegari are another strong candidates for it.

I think all the above mentioned are currently in the US. (Ngo is a sure fire; Avila comes in 2nd;) But Europe is getting very strong in math nowadays as well as Asia.

Well, I am more curious about the Chern Medal than the Fields. It seems to me somehow that this is a Prize for “an individual whose accomplishments warrant the highest level of recognition for outstanding achievements in the field of mathematics” So this means a lot. It seems to be THEEE Prize in math. I wonder who have the chances?

What do you think about one of these Bonn guys? Take for example Bringmann.