Clay Mathematics Proceedings
Volume: 4; 2005; 689 pp; Softcover
MSC: Primary 11; Secondary 14; 22
Print ISBN: 978-0-8218-3844-0
Product Code: CMIP/4
List Price: $138.00
Individual Member Price: $110.40
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Harmonic Analysis, the Trace Formula, and Shimura VarietiesShare this page
Edited by James Arthur; David Ellwood; Robert Kottwitz
A co-publication of the AMS and Clay Mathematics Institute
The modern theory of automorphic forms, embodied in what has
come to be known as the Langlands program, is an extraordinary
unifying force in mathematics. It proposes fundamental relations that
tie arithmetic information from number theory and algebraic geometry
with analytic information from harmonic analysis and group
representations. These "reciprocity laws", conjectured by Langlands,
are still largely unproved. However, their capacity to unite large
areas of mathematics insures that they will be a central area of study
for years to come.
The goal of this volume is to provide an entry point into this exciting and challenging field. It is directed, on the one hand, at graduate students and professional mathematicians who would like to work in the area. The longer articles in particular represent an attempt to enable a reader to master some of the more difficult techniques. On the other hand, the book will also be useful to mathematicians who would like simply to understand something of the subject. They will be able to consult the expository portions of the various articles.
The volume is centered around the trace formula and Shimura varieties. These areas are at the heart of the subject, but they have been especially difficult to learn because of a lack of expository material. The volume aims to rectify the problem. It is based on the courses given at the 2003 Clay Mathematics Institute Summer School. However, many of the articles have been expanded into comprehensive introductions, either to the trace formula or the theory of Shimura varieties, or to some aspect of the interplay and application of the two areas.
This book is suitable for independent study.
Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Table of Contents
Table of Contents
Harmonic Analysis, the Trace Formula, and Shimura Varieties
Graduate students and research mathematicians interested in number theory, automorphic forms, and group representations.