2010 Fields Medal (1 Viewer)

[buchanan]

Who do you think will win a Fields medal in 2010?

I reckon Ngô Bảo Châu from Vietnam will win it.

He proved the fundamental lemma of Langlands:

http://arxiv.org/pdf/0801.0446v3

This has been chosen by Time Magazine as one of the top 10 discoveries of 2009 (although it was proved in 2008, since it is a very long and hard proof, it wasn't finally verified till 2009):

The Fundamental Lemma, Solved - The Top 10 Everything of 2009 - TIME

 

[humphdogg]

I think it'd be hard to overlook Ben Green again, especially if his forthcoming paper with Terry Tao on the prime k-tuples conjecture is as good as it sounds.

 

[buchanan]

One way to help guess who will win a Fields medal at the ICM is to take a look at those on the speakers list who are under forty. Many people think Ngo is a shoo-in for his work on the fundamental lemma. He’s a plenary speaker:

International Congress of Mathematicians 2010, Hyderabad Invited Speakers

Of course, Green and others can also win it since the medal can be awarded to 2 to 4 recipients under 40. But I think it would be harder to predict who else will win it.

 

[Cazic]

Why do you think Ngô Bảo Châu will win it? Because everyone else thinks he will win it, or because you have enough of a feeling for the maths the "contenders" are doing to be able to judge?

Personally, I can't make heads or tails of the maths these guys are into so I have no idea who deserves the medal(s).

 

[buchanan]

I suggest you read the <a href="http://www.time.com/time/specials/packages/article/0,28804,1945379_1944416_1944435,00.html">Time Magazine article</a>.

It would be disappointing if he didn't get the Fields medal.

Many others would want him to get the medal:

ICM 2010 Not Even Wrong

Another thing that leads one to agree that he should get the medal is that previous recipients (in particular, Drinfeld in 1990 and Lafforgue in 2002) have also made breakthroughs on the Langlands program.

 

[humphdogg]

Considering there's an 18 page article out there just describing the Fundamental Lemma, I'd say it's pretty tough to understand (I only really have any understanding of the SL_2 case, which is pretty basic). It's hard to keep up with the maths of the "contenders" too because there are so many young mathematicians out there and very few have a high profile a la Terry Tao.

What did Drinfeld and Lafforgue prove?

 

[buchanan]

Drinfeld proved the Langlands conjectures for GL₂ of a function field.

http://www.mathunion.org/o/General/Prizes/Fields/1990/Drinfeld/page1.html

Lafforgue later proved the Langlands conjectures for GL_n of a function field.:

http://www.ams.org/notices/200210/comm-fields.pdf

http://www.ams.org/notices/200302/fea-suslin.pdf

 

[Cazic]

Considering there's an 18 page article out there just describing the Fundamental Lemma, I'd say it's pretty tough to understand (I only really have any understanding of the SL_2 case, which is pretty basic). It's hard to keep up with the maths of the "contenders" too because there are so many young mathematicians out there and very few have a high profile a la Terry Tao.

What did Drinfeld and Lafforgue prove?

You're studying maths down at ANU? How is it?

 

[humphdogg]

You're studying maths down at ANU? How is it?

Pretty awesome - it's got a great pure maths faculty (especially for analysis). Plus doing the PhB degree means you get to do graduate level stuff in an undergraduate degree, which is pretty sweet.