Conference: "Geometry and Arithmetic"

会议：“几何与算术”

• 批准号: 0456551
• 负责人: Robert MacPherson
• 金额: $ 2万
• 依托单位: Institute For Advanced Study
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-04-01 至 2006-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0456551&HistoricalAwards=false
• 关键词: Conference; Geometry; Arithmetic

A four day conference entitled "Geometry and Arithmetic" will be held during the period of October 17, 18, 19 and 20, 2005, at the Institute for Advanced Study in Princeton, New Jersey. The conference will be wide ranging in subject matter, including talks in algebraic geometry, number theory, automorphic forms, and representation theory. All of these fields were influenced by the new techniques introduced by Deligne and Grothendieck (such as etale cohomology, motives, sheaf theoretic methods for both coherent sheaves and constructible sheaves, the derived category, mixed Hodge theory). The aim of the conference is to allow mathematicians from these fields to interact with each other in a constructive manner.Beginning in the 1960's, a powerful collection of new ideas emerged in Paris, developed by the mathematicians Pierre Deligne and Alexander Grothendieck. These ideas grew from algebraic geometry, a field that was then somewhat arcane and isolated from the rest of mathematics. The Deligne-Grothendieck ideas were so powerful and wide reaching that, in the years since their inception, they have found essential applications in very different areas, such as number theory (the study of equations involving whole numbers) and group theory (the study of symmetries). They have played a major unifying role in mathematics. Now, Deligne has moved to the United States and we hope that this conference, celebrating his achievements, will contribute in its own small way to unifying mathematics

为期四天的会议，题为“几何和算术”将在2005年10月17日，18日，19日和20日在新泽西州普林斯顿的高级学习研究所举行。 会议将在主题上广泛，包括代数几何，数字理论，自动形式和代表理论的谈话。 所有这些领域都受到了Deligne和Grothendieck引入的新技术的影响（例如，依托的共同体，动机，动机，捆捆的理论方法和可构造的滑轮，衍生的类别，混合Hodge理论）。 会议的目的是允许这些领域的数学家以建设性的方式相互互动。在1960年代，数学家Pierre Deligne和Alexander Grothendieck开发了1960年代，在巴黎出现了强大的新想法。 这些想法源自代数几何形状，该领域在某种程度上是一个神秘的，并且与其他数学的数量隔离开来。 Deligne Grothendieck的想法是如此强大和广泛，以至于自成立以来的几年中，他们在非常不同的领域中发现了必不可少的应用，例如数字理论（涉及整数的方程式研究）和群体理论（对称性的研究）。他们在数学中发挥了重要的统一作用。 现在，迪格尼（Deligne）已搬到美国，我们希望这次会议庆祝他的成就，将以自己的小型方式做出贡献，以统一数学