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

NSF/CBMS 数学科学区域会议 - 遍历拉姆齐理论：静态定理的动态方法 - 2008 年夏季

• 批准号: 0735307
• 负责人: Patrick Coulton
• 金额: $ 2.73万
• 依托单位: Eastern Illinois University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0735307&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

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.

遍历拉姆齐理论是1977年由H. Furstenberg证明了经典的庞加莱递归定理的一个深远的扩展，并从这个扩展Szemeredi定理导出。Furstenberg的方法Szemeredi的定理不仅揭示了动力学的基础，这个看似静态的结果，但它也表明了一种方法，迅速导致令人印象深刻的进展，如Furstenberg-Katznelson的多维扩展Szemeredi的定理，Bergelson-Leibman的多项式扩展Szemeredi的定理和Hales-Jewett定理以及最近壮观的工作B。绿色和T.这次会议的题目是“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。 维塔利Bergelson将给一系列的十个讲座提供了一个主题的概述和必要的背景，以促进在这个发展中的领域的研究。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。一个特别的努力将作出强调许多自然的新方向的研究，使他们有吸引力的年轻数学家。维塔利Bergelson，前学生的哈利Furstenberg，已交付讲座和迷你课程的主题遍历拉姆齐理论在许多会议和研讨会。2006年在马德里举行的国际数学家大会上，他应邀在“常微分方程和动力系统”一节发表演讲。Bergelson教授在遍历拉姆齐理论、组合数学和多重递归理论等领域发表了大量著作。Vitaly Bergelson目前是俄亥俄州州立大学的教授。