Thursday, August 19, 2010

Fields Medals Awarded for Work in Number Theory, Ergodic Theory, and Statistical Physics

The Fields Medals in mathematics were announced today. One of them was awarded for research in number theory, one of them was awarded for work in ergodic theory (an area of dynamical systems) with connections to number theory, and two of them were awarded for theoretical work in statistical physics. As you can see, three of these are parts of fields that are near and dear to my heart.

The new Fields Medalist who does some work in dynamical systems is Elon Lindenstrauss, who I met at the Penn State--University of Maryland spring dynamical systems meeting in 2001. I knew he was very good, and he's done some very nice stuff over the years, but it didn't occur to me that he might win a Fields Medal for it. I haven't seen him since that meeting, but he struck me then as a very humble person, so hopefully his subsequent decade of amazing success hasn't changed him. Lindenstrauss got his award for progress on the Littlewood conjecture. He also is one of the people responsible for the only truly huge result in quantum chaos from the last decade or so (and probably from somewhat longer than that, depending on how one wants to count things), which was a proof (with Jean Bourgain) Zev Rudnick's and Peter Sarnak's Arithemetic Quantum Unique Ergodicity conjecture. This result was mentioned explicitly in the citation but seems to have been a secondary consideration in the award.

You can find the official prize announcements at this website.

Update (8/20/10): Here is another brief article, which makes the excellent point that some of the work of this year's Fields medalists has more applied implications than is usually the case. These four people are still very much pure mathematicians---I prefer the term "theoretical mathematician" to "pure mathematician", by the way---but this (in addition to the interest I have in the subject areas of the Medalists) still warms my heart.

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