Archive for August 14th, 2014

ICM2014 — Avila laudatio

August 14, 2014

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 are given a differential equation, and you try to find solutions. This has of course had a number of amazing successes.

2. However, after a while it became clear that the differential equations for which one could hope to find a solution were not typical. The next stage, initiated by Poincaré, was to aim for something less. One could summarize it by saying that now, given a differential equation, one tries merely to say something interesting about its solutions.

3. In the 1960s, Smale and Thom went a stage further, trying to take on board the realization that often physicists don’t actually know the equation that models the phenomenon they are looking at. As Ghys put it, the endeavour now can be summed up as follows: you are not given a differential equation and you want to say something interesting about its solutions.
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