NSF/CBMS Regional Conference in the Mathematical Sciences - "The Web of Modularity"

该奖项将资助一个名为“模块化网络”的NSF-CBMS区域研究会议，该会议将于2003年夏天在伊利诺伊大学厄巴纳-香槟分校举行。会议的讲师将是威斯康星大学麦迪逊分校的小野肯教授；小野教授将围绕模形式理论在数论相关的各个数学领域中所扮演的不同角色进行10场讲座。会议将集中讨论一系列广泛的问题，这些问题可以通过使用模块化形式加以解决。这些问题包括表示论、配分论、算术几何、l函数理论、超几何级数和组合学。虽然这些包含了数学研究活跃领域中非常广泛的主题，但它们的共同特点是可以使用模形式理论的统一技术集来理解。会议的主要目标是：1)对模块形式在数论和其他数学领域中发挥的重要和多样化作用进行有组织和有动机的描述。2)为年轻的数学家和刚进入该领域的人（特别是研究生和博士后）提供关于该研究领域前沿的重要技术、定理和开放问题的通俗易懂的描述。3)为成熟的研究人员提供一个分享他们的专业知识和相互交流的机会，并与年轻的数学家交流。4)加强在会议主题相关领域工作的研究人员之间的区域联系。5)计划一项科学计划，该计划将导致出版对更广泛的数学界具有持久重要性的专著。

This award will fund an NSF-CBMS Regional Research Conference entitled ``The Web of Modularity''to be held at the University of Illinois at Urbana-Champaign in the summer of 2003. The conference lecturer will be Professor Ken Ono of the University of Wisconsin at Madison; Professor Ono will give ten lectures centered around the diverse roles which the theory of modular forms plays in various areas of mathematics related to Number Theory. The conference will focus on a wide array of problems which can be addressed through the use of modular forms. These include, among others, problems from representation theory, partition theory, arithmetic geometry, the theory of L-functions, hypergeometric series, and combinatorics. Although these comprise a very broad array of topics in active areas of mathematical research, they share the feature that they can be understood using a unified set of techniques from the theory of modular forms.The main goals of the conference are:1) To present an organized and motivated description of the important and diverse role which modular forms play in Number Theory and other areas of mathematics.2) To provide young mathematicians and newcomers to the field (particularly graduate students and post-docs)with an accessible account of important techniques, theorems, and open problems at the forefront of this area of research. 3) To provide established researchers an opportunity to share their expertise and to interact with each other and with junior mathematicians.4) To strengthen regional ties among researchers working in areas connected to the themes of the meeting.5) To plan a scientific program which will lead to a published monograph of lasting importance to the wider mathematical community.