Travel support for a CRM Research Program in Arithmetic Geometry of function fields of positive characteristic

该项目将支持美国研究人员于2010年春季在西班牙巴塞罗那的“数学研究中心”（CRM）参加一个关于正特征函数场的算术几何的国际项目。该项目将包括研究生课程、两个国际研讨会和一个关于最新发展的高级课程。预计来自世界各地的研究人员将参加会议，一些课程和研讨会的笔记将会出版。算术几何是利用代数几何的方法和工具研究起源于数论的问题。该领域最近取得了惊人的进展（如费马大定理的证明），并将其应用于可靠的通信和信息安全等当代技术。从算术结构（如有理数）和更多几何结构（如直线上的多项式函数）之间的类比和相互作用中获得了大量的洞察力。本次研讨会将继续探索这些类比和相互作用。

This project will support US-based researchers attending an international program on the arithmetic geometry of function fields of positive characteristic at the "Centre de Recerca Matematica" (CRM) in Barcelona, Spain, during the spring of 2010. The program will include graduate courses, two international workshops, and an advanced course on recent developments. It is expected that researchers from around the world will attend and that notes from some of the courses and workshops will be published.Arithmetic geometry is the study of questions originating in number theory using the methods and tools of algebraic geometry. The field has seen recent spectacular advances (such as the proof of Fermat's Last Theorem) and applications to contemporary technologies such as reliable communications and information security. A great deal of insight has been gained from the analogies and interactions between arithmetical structures (such as the rational numbers) and more geometric structures (such as polynomial functions on the line). This workshop will continue the exploration of these analogies and interactions.