SM-Special Year in Arithmetic Geometry at the CRM Barcelona

SM-巴塞罗那 CRM 算术几何特别年

• 批准号: 0963919
• 负责人: Wayne Raskind
• 金额: $ 2万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-05-01 至 2011-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0963919&HistoricalAwards=false
• 关键词: SM; Special; Year; Arithmetic; Geometry

This grant will support US-based speakers and other US-participants to attend the conference, Regulators III, to take place in July 2010 at the Centre de Recerca Matematica (CRM) in Barcelona, Spain. This is the culminating conference of a year-long program in arithmetic geometry at the CRM, and will attract many of the best researchers in the world. The funding will allow US-based researchers to learn of the latest developments in a field in which mathematicians from Europe and Asia have been playing an increasing role over the last 10 years. Recent developments in the subject include work on Beilinson?s conjecture on special values of L-functions of certain automorphic representations of a symplectic group in four variables, and the lack of surjectivity of certain regulators for generic surfaces of degree at least 5 in projective 3-space over p-adic fields. Regulators help to measure the size of objects in arithmetic and geometry, and they are a unifying theme in the subject. The definition and computation of regulators is a fundamental part of several parts of mathematics. One recent theme in the subject has been to transport techniques from arithmetic to geometric situations, and vice-versa. These methods have allowed us to demonstrate the existence of interesting elements of important arithmetic and geometric objects.

这笔赠款将支持美国的演讲者和其他美国参与者参加将于 2010 年 7 月在西班牙巴塞罗那 Centre de Recerca Matematica (CRM) 举行的 Regulators III 会议。 这是 CRM 为期一年的算术几何项目的高潮会议，将吸引世界上许多最优秀的研究人员。 这笔资金将使美国研究人员能够了解欧洲和亚洲数学家在过去十年中发挥着越来越重要作用的领域的最新发展。 该主题的最新进展包括贝林森关于四个变量中辛群的某些自守表示的 L 函数的特殊值的猜想，以及 p 进场上的射影 3 空间中至少 5 次的泛型曲面的某些调节器的满射性的缺乏。 调节器有助于测量算术和几何中物体的大小，它们是该学科的统一主题。 调节器的定义和计算是数学几个部分的基础部分。 该主题最近的一个主题是将技术从算术情况转移到几何情况，反之亦然。 这些方法使我们能够证明重要算术和几何对象的有趣元素的存在。