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As is now widely reported, the Fields medals for 2010 have been awarded to Elon Lindenstrauss, Ngo Bao Chau, Stas Smirnov, and Cedric Villani. Concurrently, the Nevanlinna prize (for outstanding contributions to mathematical aspects of information science) was awarded to Dan Spielman, the Gauss prize (for outstanding mathematical contributions that have found significant applications outside of mathematics) to Yves Meyer, and the Chern medal (for lifelong achievement in mathematics) to Louis Nirenberg. All of the recipients are of course exceptionally qualified and deserving for these awards; congratulations to all of them. (I should mention that I myself was only very tangentially involved in the awards selection process, and like everyone else, had to wait until the ceremony to find out the winners. I imagine that the work of the prize committees must have been extremely difficult.)
Today, I thought I would mention one result of each of the Fields medalists; by chance, three of the four medalists work in areas reasonably close to my own. (Ngo is rather more distant from my areas of expertise, but I will give it a shot anyway.) This will of course only be a tiny sample of each of their work, and I do not claim to be necessarily describing their “best” achievement, as I only know a portion of the research of each of them, and my selection choice may be somewhat idiosyncratic. (I may discuss the work of Spielman, Meyer, and Nirenberg in a later post.)