SM-Special Year in Arithmetic Geometry at the CRM Barcelona

这笔赠款将支持美国的发言者和其他美国参与者参加2010年7月在西班牙巴塞罗那的Centre de Recerca Matematica（CRM）举行的监管机构III会议。 这是CRM算术几何为期一年的计划的高潮会议，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能够了解欧洲和亚洲数学家在过去10年中发挥越来越大作用的领域的最新发展。 最近的事态发展，在这个问题上，包括工作贝林森？的猜想，以及p-adic域上射影3-空间中至少5次一般曲面的某些调节子的满射性的缺乏。 在算术和几何中，调节器有助于测量物体的大小，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的几个部分的基本组成部分。 最近的一个主题是运输技术从算术几何的情况下，反之亦然。 这些方法使我们能够证明存在的重要算术和几何对象的有趣的元素。

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.