ICM2014 — Khot laudatio

Originally posted on Gowers's Weblog:

After McMullen’s laudatio on Mirzakhani, it was time for Sanjeev Arora to talk about the work of the Nevanlinna prize winner Subhash Khot. It was also the time that a significant proportion of the audience decided that enough was enough and left the room. The same thing happened in Hyderabad four years ago, and on both occasions I was fairly shocked: I think it shows a striking disrespect, not so much for the speaker and prizewinner, though there is that aspect too, as for theoretical computer science in general. It seems to say, “Right, that’s the interesting prizes over — now we’re on to the ones that don’t really matter.” Because I have always been interested in computational complexity and related areas, my interest in the Nevanlinna prize is comparable to my interest in the Fields medals — indeed, in some ways it is greater because there is more chance…

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ICM2014 — Bhargava laudatio

Originally posted on Gowers's Weblog:

I ended up writing more than I expected to about Avila. I’ll try not to fall into the same trap with Bhargava, not because there isn’t lots to write about him, but simply because if I keep writing at this length then by the time I get on to some of the talks I’ve been to subsequently I’ll have forgotten about them.

Dick Gross also gave an excellent talk. He began with some of the basic theory of binary quadratic forms over the integers, that is, expressions of the form $latex ax^2+bxy+cy^2$. One assumes that they are primitive (meaning that $latex a$, $latex b$ and $latex c$ don’t have some common factor). The discriminant of a binary quadratic form is the quantity $latex b^2-4ac$. The group SL$latex _2(mathbb{Z})$ then acts on these by a change of basis. For example, if we take the matrix $latex begin{pmatrix}2&15&3end{pmatrix}$, we’ll replace $latex (x,y)$…

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ICM2014 — Avila laudatio

Originally posted on Gowers's Weblog:

As I said in my previous post, I don’t think I’m going to try all that hard to explain the work of the prizewinners, since it has been very well explained in other places (except that much more attention has gone to the Fields medallists than to the Nevanlinna prize winner — maybe I’ll try to redress the balance a little bit there). Instead, I’d just like to mention a few things that I found interesting or amusing during the laudationes.

The first one was an excellent talk by Etienne Ghys on the work of Artur Avila. (The only other talk I’ve heard by Ghys was his plenary lecture at the ICM in Madrid in 2006, which was also excellent.) It began particularly well, with a brief sketch of the important stages in the history of dynamics. These were as follows.

1. Associated with Newton is the idea that you…

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ICM: Fields Medal 2014

ICM = International Conference of Mathematics

It is held every 4 years, this year in South Korea, where they announce the Fields Medalists (equivalent to Nobel Prize of Maths) for the greatest Mathematicians aged below 40.

Three Chinese Fields Medalists so far:

1. ST Yao 丘成桐 (HK -> USA)
2. Terrence Tao 陶軒哲 (HK -> Australia),
3. Bao-Chao Ngo 吴宝珠 (Vietnamese Chinese –> France@ École Normale Sup).

Surprise! The first lady Fields Medalist in history, Maryam Mirzakhani, a Harvard PhD and now a Stanford professor, is from Iran.

image

The Indian Fields Medalist Bhargava is a Princeton professor, a Canada/ American.  

Two of the Fields medalists (Maryam Mirzakhani and Artur Avila ) were IMO Gold medalists, with Maryam Mirzakhani twice perfect scores (42/42 world’s 1st in 1994 and 41/42 in 1995), Artur Avila (Brazil, 1995, 37/42 scores, ranked 23rd). Hard to understand she did not do well in Math in school initially in Iran,  because she was not interested in Math then.

http://www.theguardian.com/science/2014/aug/13/fields-medal-mathematics-prize-woman-maryam-mirzakhani

The other two are Martin Hairer from  (Austrian- UK ) and Artur Avila from (Brazil – France). Bhargava and Hairer didn’t participate in any IMO.

IMO seems to indicate the potential Fields medalists, but it is not a sufficient condition. IMO Math solves problems with known solution within hours; Fields Math solves problems with unknown solution which requires many years of research and perseverance.

Many Fields medalists have warned, especially in China, that IMO is bad for Math – one Hua Luogeng’s former student had said IMO Math is like “acrobatic to real kungfu” – looks alike but unreal.