Conference: "Geometry and Arithmetic"

题为“几何与算术”的会议将于2005年10月17日、18日、19日和20日在新泽西州普林斯顿高等研究院举行，为期四天。会议主题广泛，包括代数几何、数论、自同构形和表示论的演讲。所有这些领域都受到了Deligne和Grothendieck提出的新技术的影响(如上同调、动机、凝聚层和可构造层的层理论方法、派生范畴、混合Hodge理论)。会议的目的是让来自这些领域的数学家以建设性的方式相互交流。从20世纪60年代的S开始，由数学家皮埃尔·德莱恩和亚历山大·格罗森迪克发展起来的强大的新思想集合在巴黎出现。这些想法源于代数几何，这个领域当时有点神秘，与其他数学学科隔绝。Deligne-Grothendieck的思想是如此强大和广泛，以至于在它们诞生以来的几年里，它们在非常不同的领域找到了基本的应用，例如数论(研究涉及整数的方程)和群论(研究对称性)。它们在数学中起到了重要的统一作用。现在，Deligne已经搬到了美国，我们希望这次会议，庆祝他的成就，将以自己的小方式为统一数学做出贡献

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