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

遍历拉姆齐理论起源于1977年，H. Furstenberg证明了经典庞加莱递归定理的一个深远推广，并从这个推广中导出了Szemeredi定理。Furstenberg对szmeredi定理的研究不仅揭示了这个看似静态结果的动态基础，而且还指出了一种方法，这种方法很快导致了令人印象深刻的进步，例如Furstenberg- katznelson对szmeredi定理的多维扩展，Bergelson-Leibman对szmeredi定理的多项式扩展和Hales-Jewett定理，以及最近B. Green和T. Tao关于素数的算术数列的惊人工作。会议的题目是“遍历拉姆齐理论：静态定理的动态方法”。会议将于2008年6月22日至6月28日举行。Vitaly Bergelson将提供一系列十次讲座，概述该主题以及促进这一发展领域研究所必需的背景。会议的主题将吸引在组合学、数论和动力系统方面工作的不同研究人员。我们将特别努力强调许多自然的新研究方向，并使它们对年轻数学家具有吸引力。Vitaly Bergelson曾是Harry Furstenberg的学生，在许多会议和研讨会上发表过关于遍历拉姆齐理论的讲座和迷你课程。2006年在马德里举行的国际数学家大会上，他在“常微分方程和动力系统”部分发表了应邀演讲。Bergelson教授在遍历拉姆齐理论、组合学和多次递归理论等领域发表了大量论文。Vitaly Bergelson目前是俄亥俄州立大学的教授。

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.