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

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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.