ICM2010 — Nirenberg and Meyer laudationes

Normally at an ICM the first day has its own very distinct atmosphere because of the opening ceremony, the laudationes, and so on, after which the congress settles into a more regular, working format, with plenary lectures in the morning and invited lectures in parallel sessions in the afternoon. This year, because the number of prizes has increased and one of them needed inaugurating, some of the first-day feeling continued into the second day. And because my panel discussion was in the afternoon and lasted two hours, I had to miss the parallel sessions, so I personally had no sense of the ICM having properly started until the third day.

ICM2010 — Chern prize inauguration

Yesterday I wrote a post in the Rajiv Gandhi International Airport in Hyderabad. I couldn’t post it there because I wasn’t connected, but Dubai airport had free wi-fi so I could finish the job a few hours later. The ICM interrupted a holiday I was having in the South of France with my wife’s family, so now, after a refreshing four-hour night, I find myself at 6.30am in the rather less glamorous Luton airport, stupidly early for a flight on a rather less glamorous airline than Emirates, with whom I flew to Hyderabad and back. Talking of stupid punctuality, there’s a maxim I quite like, which is probably very well known but I heard it only within the last year or two, which is that if you have never missed a plane then you spend too much of your life in airports. I like the maxim, but I don’t live by it, because I have an irrational dread of missing planes, and an entirely rational lack of dread of spending time in airports — if all else fails, they are a pretty good place to do mathematics. Today, all else has not failed, since I have a charged up computer (that’s an issue these days — I think my laptop is due a new battery) and multiple blog posts to write. I haven’t quite decided what form these will take: I cannot possibly write about days 2-4 in the same amount of detail as I have written about day 1, but once I start, it is hard to stop. So do I prefer to keep up the detail and risk stopping in the middle of day 2, or to force myself to become a bit sketchier? Perhaps I’ll be detailed, but more selective about what I write about.

ICM2010 — rest of day one

As I write this I'm sitting in the Rajiv Gandhi international Aiport waiting for a flight to Dubai. The ICM lasts till Friday, but for me it is over: with a son of two and a half, there are limits to how long it is reasonable to be away, and the marginal utility of the ICM has dipped below the marginal cost of staying away (or rather, that is how I judged it in advance). Actually, today (Monday the 23rd) is the half-way point and is a free day. Most of the delegates, to judge from the people I've spoken to, are taking the opportunity to go on ICM-organized tours. It is pretty tantalizing not to be doing that myself, but I leave India with a huge affection for the country and a strong sense that I'll be back.

Listening to five laudationes in a row is pretty gruelling — as I know from having done it five times now. After they were over, Assaf Naor asked whether I wanted to go and get a cup of coffee somewhere, or whether I would be listening to the talk by Varadhan, a recent Abel prize winner. To make my decision easier, he explained that he himself was skipping the talk only because he had heard it before, and he knew that it was excellent. I hesitated, and in the end decided that self-preservation was in order, a principle that I continued to adopt later. By that I mean that if you go to every talk that has a good chance of being superb, plus every talk that is sufficiently noteworthy that you don't want to miss it even if it is terrible, then you end up utterly exhausted. Because the laudationes had started late, there was very little break between them and the beginning of Varadhan's talk, and I just couldn't face three and half hours, or whatever it would have been, of continuous talk. The difference between this ICM and previous ICMs is that these little decisions of mine, which I normally like to make rather discreetly (which is particularly easy for parallel sessions, because you might always be at a different talk), are now completely public. But I think I'm ready to live with this.

ICM2010 — Spielman laudatio

I’ve saved the best till last, which should not be taken as a negative comment about the other laudationes, since Gil Kalai’s was a tour de force. His first distinction was that he was the only one of the five speakers not to be wearing a tie. He was, however, wearing a suit, so the result was to look smart in a trendy way rather than smart in a more standard mathematician-giving-important-talk way. And he opened his talk daringly with the promise that his would be a comprehensible talk, which got a laugh from the audience.

On a more negative note, I was a bit shocked that a significant proportion of the audience got up to leave before he started, as if to say, “The real business is over — this is just the Nevanlinna prize.” All I can say is that it was their loss, not just because of the wonderful talk but also because of the wonderful mathematics described in the talk.

ICM2010 — Villani laudatio

The first thing that stood out when H-T Yau got up on to the stage was his relative youth. (I’ve just looked him up and he was born in 1959.) He began with an amusing quote from von Neumann, who advised Shannon to use the word “entropy” on the grounds that “Nobody knows what entropy really is, so in a debate you will always have the advantage.” Part of the reason von Neumann said that was that there has always been a tension between the irreversible nature of entropy and the reversibility of the Newtonian mechanics that is supposed to underpin it. How can the two be reconciled? My impression is that this quaisi-philosophical problem has largely been sorted out (so in particular, I’m not about to say that Villani has “solved the mystery of entropy” or something like that). In fact, let me reproduce Yau’s list of Villani’s three major achievements.

1. He established a rigorous connection between entropy and entropy production. (I don’t actually quite know what he meant by this.)

2. He established entropy as a fundamental tool in optimal transport, and curvature in metric spaces.

3. He rigorously proved a phenomenon known as Landau damping, a very surprising decay of the electric field in a plasma without particle collisions (and therefore without entropy increase).

I’ve just looked at Tao’s post on the Fields medallists and my understanding is such that I’m not even quite certain which of the above three achievements he is describing in detail. (That’s a comment about the headings — Tao writes with his usual clarity.)

ICM2010 — Smirnov laudatio

Next, Kesten shuffled on to the stage. He has an unusual face, in that he has a white beard of the kind that looks as though it is never trimmed — indeed, I think that is probably the case, given the way it grows out sideways as well as down — and looks slightly fake, to the point where one cannot help imagining what he would look like without it, to which the answer is that he would probably look a lot younger as the hair on the top of his head is black. (As I write this, in a large room with dozens of terminals, he has just walked in.)

He began by telling us that Smirnov had got perfect scores in the International Mathematical Olympiads in 1986 and 1987, just in case we were in any doubt about his mathematical talents. His next remark came as a very pleasant surprise: even since the committee had made its decision — in fact, in the last two months — Smirnov had proved a major result. Let me begin by saying what that was.

ICM2010 — Ngô laudatio

Before I continue with brief descriptions of the laudationes, let me mention that Julie Rehmeyer has written descriptions of their work for a general audience and Terence Tao has now posted about the work of the Fields medallists and the other prizewinners. And as I have already said, the ICM website has links to the full texts of the laudationes themselves. So anybody now wanting to understand the mathematics has an excellent starting point, and I am free to concentrate on the more frivolous details of the talks, perhaps slipping in the odd mathematical comment as I do so.

Jim Arthur went next. His was the terrifying task (though much less terrifying for him than for most) of explaining the work of Ngô Bảo Châu to a general mathematical audience. I’d say that he did about as well as it is possible to do, which meant that he was able to convey some of the flavour, but obviously without managing to transmit to the non-expert the sort of wisdom tht it takes the experts in this particular area years to accumulate.

ICM2010 — Lindenstrauss laudatio

After the unceremonial closing of the opening ceremony it was lunch time. I soon found myself in the first of what would turn out to be many queues of the kind where the optimal strategy is far from obvious but obviously not very good. One of the army of volunteers (the males of whom were wearing smart purple Indian shirts — collarless and going down to the thigh) told me to go up a floor, so I did, and I found a number of parallel queues. There was also a borderline-legitimate queuelet round to the side, and I joined that, hoping that it was legitimate enough not to annoy people and not too far to the side to get the attention of the people serving lunch. Lunch was basically an Indian takeaway — a choice of various Indian dishes served in an aluminium tray and a white cardboard lid that was rectangular apart from being curved off at the vertices, and held in place by a fold at the top of the aluminium. (I’m not certain it was aluminium but that’s my best guess.) After about 15 minutes of anxious waiting I was in a position to ask for lamb biryani, which I had also had for breakfast. It cost me two coupons from my kit bag, and came with a small pot of yoghurt, and the option of a fierce looking chutney, which I took. (I was about to say “took with relish” but then realized that to some people that would be ambiguous.) I was told that if I wanted to sit down I could go into the gallery of the main hall, so I did. A table would have been nice, but I could manage without.

The lamb biryani was slightly disappointing in that it had just one piece of lamb which, though large, was about 80% bone. That left quite a lot of rice to get through, and I was glad of the opportunity to spice it up with the chutney. For what it’s worth, we were provided with small wooden disposable spoons and forks to eat with. The chutney passed a basic test: it made my nose run.

ICM2010 — Opening ceremony, continued

I’d got up to the awarding of the Nevanlinna prize to Dan Spielman. Next up was the Gauss prize. Yves Meyer came up on stage with a dark blue jacket and dark grey trousers (both dark enough that you had to look hard to see that they didn’t form a suit). We were told that he had “created a new way of multiresolution thinking,” a conclusion that would be hard to dispute. He had a grey beard and moustache and a vigorous handshake. This was the second ever Gauss prize, the first going to Ito in Madrid in 2006.

An even newer prize followed, the first award of the new Chern prize for lifetime achievement. This is an interesting prize in that it comes with a lot of money — half a million dollars (some of it from Chern’s family and some from the Simons foundation, about which more later) — which is split 50-50 between the recipient and good mathematical causes nominated by the recipient. I wonder if we will get to hear how Nirenberg decides to spend the charitable half. (Update: I’ve just discovered on the web that he’s giving it to the Courant Institute.) Nirenberg had white hair, beard and moustache, and did not smile.

After that was all over, the president (of India, not the IMU) told us once again what the ICM was, but after that unpromising start she moved into a speech about India’s mathematical heritage and various other topics, all discussed in a way that made it clear that somebody — I presume not her — knew what they were talking about. She told us of an old Sanskrit saying, “Mathematics stands at the helm of all sciences.” I think I prefer the “queen of” metaphor that is more prevalent in the west. She told us that the concept of zero originated in India, and that calculus was anticipated in India in the 15th century. I wondered before the opening ceremony started how many times Ramanujan would be mentioned. There was a mention here, and a few others, but I forgot to count. At one point the president referred to India’s rich cultural heritage twice in successive sentences. There was plenty about the impact of mathematics in technology, economics, cultural life — you get the idea. But this was a pretty good speech as such things go, and the president seemed intelligent, and young for her years.

ICM2010 — more on the opening ceremony

Let me try to give a stream-of-consciousness description of the opening ceremony, by which I mean translate the notes I feverishly took into continuous prose and not do much else to them.

I booked my hotel fairly late in the day, for the obvious reason that if I left it longer, the work needed would be identical but I would have less choice. And so it turned out: instead of staying in the hotel right next to the congress (so much so that you can get from one to the other without going out of doors) I am, as I mentioned in my first post, about 40 minutes away. The disadvantages of this are obvious — I can’t nip back to my room to get something, and I have to worry each day about how I’m going to get to and from the hotel. But the hotel itself is nice, and I quite like getting to know the city a bit rather than being cocooned in the conference area the whole time.

This morning they laid on buses to take people from the hotels to the congress (as they will every morning). I had had dire warnings about traffic, and been told to expect a two-hour journey, which would still have been quick enough to get to the opening ceremony on time but would have left me slightly anxious. As it was, the journey took the usual 40 minutes or so, so I got to the HICC at about 8.30. We had been told to be in our seats by 10.30, so I thought I had a couple of hours to kill. However, this turned out to be a miscalculation on my part.