NSF/CBMS Regional Conference in the Mathematical Sciences - Ergodic Ramsey Theory: A Dynamical Approach to Static Theorems - Summer 2008

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Ergodic Ramsey theory was initiated in 1977 when H. Furstenberg proved a far reaching extension of the classical Poincare recurrence theorem and derived from this extension Szemeredi's theorem. Furstenberg's approach to Szemeredi's theorem not only revealed the dynamical underpinnings of this seemingly static result, but it also indicated a method which quickly led to impressive advances such as Furstenberg-Katznelson's multidimensional extension of Szemeredi's theorem, Bergelson-Leibman's polynomial extensions of Szemeredi's theorem and the Hales-Jewett theorem as well as the recent spectacular work of B. Green and T. Tao on arithmetic progressions in primes.The conference title is "Ergodic Ramsey Theory: A Dynamical Approach to Static Theorems." The conference will run from June 22 to June 28, 2008. Vitaly Bergelson will give a series of ten lectures providing an overview of the subject and the background necessary to promote research in this developing field. The subject of the conference will appeal to a diverse group of researchers working in combinatorics, number theory and dynamical systems. A special effort will be made to emphasize the many natural new directions of research and to make them attractive to young mathematicians.Vitaly Bergelson, a former student of Harry Furstenberg, has delivered lectures and mini-courses on the topic of Ergodic Ramsey theory at numerous conferences and workshops. He delivered an invited talk in the section "Ordinary Differential Equations and Dynamical Systems" at the International Congress of Mathematicians in Madrid in 2006. Professor Bergelson has published extensively in the areas of Ergodic Ramsey Theory, combinatorics and the theory of multiple recurrence. Vitaly Bergelson is currently a professor at the Ohio State University.