SM-Special Year in Arithmetic Geometry at the CRM Barcelona

这笔拨款将支持美国的演讲者和其他美国参与者参加2010年7月在西班牙巴塞罗那的Recerca Matematica （CRM）中心举行的第3届监管机构会议。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好的研究人员。这笔资金将使美国的研究人员了解这一领域的最新发展，在过去10年里，欧洲和亚洲的数学家在这一领域发挥着越来越大的作用。该学科的最新进展包括对贝林森？关于四变量辛群的某些自同构表示的l -函数的特殊值的猜想，以及射影3-空间p进域上至少5次的一般曲面的某些调节器的满射性的缺乏。监管机构帮助用算术和几何来衡量物体的大小，它们是这门学科的一个统一主题。调节器的定义和计算是数学中几个部分的基础部分。这门学科最近的一个主题是从算术到几何情况的转换技术，反之亦然。这些方法使我们能够证明重要的算术和几何对象的有趣元素的存在。

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.