The Infinite Wall

I - only I - the Nothing and the Infinite in one. Climbing the infinite wall.

Wednesday, May 24, 2006

The Abel prize for 2006

You have a needle lying in the plane, and your job is to turn it 180 degrees. However: When a needle is turned, it swipes out an area, and in addition to turning the needle (easy job), you are supposed to do it while swiping out the minimal possible area (harder job). This is a special case of the Kakeya problem, an area where the the Abel prize winner this year, Lennart Carleson has made important contributions.
"The Abel prize?" I can hear you asking, "what is so special about that?" Well, it's what mathematics has always been missing: A major, central prize for long-time, outstanding achievement that is recognized in the mathematical community - on par with the Nobel prize in physics. The award is roughly a million dollars (6000000 Norwegian kroner), and was awarded for the fourth time this year. Unlike the Nobel prize, which is funded from Nobel's private fortune, the prize fund is a huge grant from the Norwegian government. I was told so by my "thesis grandfather" (my thesis advisor's thesis advisor), who happened to sit next to me on the ceremonies. He was instrumental in obtaining the grant, he told me, and explained how the prize fits into a larger picture of inspiring everyone - in Norway and elsewhere; from researchers to first graders - to enjoy and excel in mathematics.

I hadn't really looked forward to the formal ceremony on the 23rd of May, and was in it all for the lectures, but I was positively surprised and would attend again. I will in particular remember the prize winner's description of mathematics as an eternal building all mathematicians take part in constructing, and his warning not to let the children feel that their place in that house is, as one elementary school pupil told him "in the basement, staring at a wall".
The highlight, the lectures, were held on the 24th of May. I enjoyed them all, but could only follow them more to varying degrees. Lennart's own talk was a bit on the unstructured side, and he seems to have misunderstood the time allotted, as he kept glancing nervously on the wall clock while still having more than half an hour left. He finished well ahead of time. His talk was very inspirational, though, and a good survey. I'm taking some of his incidental remarks with me home as valuable luggage.
The talk I enjoyed the most was held by Oded Schramm - obviously because it was close to my own field. He talked about percolation theory, a theory that on the surface looks very easy, but which contains deep and difficult results. As an intro: Take a piece of square ruled paper, and label the intersections nodes and the lines connecting them vertexes. A: Using some random number generator like a coin, a die or suchlike, fix a number N, and flip for each vertex. If you flipped a number above N, mark that vertex. When you're done, you have a funny, random graph in front of you. Look for maximal connected shapes in it. B: Flip for the nodes instead of the vertexes, and link up neighbouring nodes if they both have been chosen. Look for maximal connected shapes. In percolation theory, the search is for what probabilities would give you infinite connected graphs (shapes) within various graphs that look a bit like an infinite extension of the paper in front of you.
Schramm also had the dubious pleasure of being cornered by yours truly during the Abel prize party, which again was more interesting than I had imagined. Some nice entertainment and most certainly higher class wine than what is served the parties I usually attend. Aside from learning a bit, I showed Oded Schramm how to draw square roots manually and how this is a very simple operation in binary. It turned out that he was into mountaineering, so we shared some stories and experiences there.
But I am digressing, am I not? Well, the story of the Abel prize is over for this year. I hope it will attract the attention it deserves, on par with the Nobel prize, and I hope to do my little share by telling you about it.
As for me, I will keep working on the impulses I got both in the formal setting via Carleson and Schramm, and more informally by having lunch with Klara Hveberg, with whom I share mathematical genealogy through our common thesis advisor Tom Lindström. Klara gave me a copy of her thesis, which is within my own field, and I have already found some formulations in it that appear useful to my own work.


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