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Harmonic Analysis, the Trace Formula, and Shimura Varieties
 
Edited by: James Arthur University of Toronto, Toronto, ON, Canada
David Ellwood Clay Mathematics Institute, Cambridge, MA
Robert Kottwitz University of Chicago, Chicago, IL
A co-publication of the AMS and Clay Mathematics Institute
Harmonic Analysis, the Trace Formula, and Shimura Varieties
Softcover ISBN:  978-0-8218-3844-0
Product Code:  CMIP/4
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Harmonic Analysis, the Trace Formula, and Shimura Varieties
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Harmonic Analysis, the Trace Formula, and Shimura Varieties
Edited by: James Arthur University of Toronto, Toronto, ON, Canada
David Ellwood Clay Mathematics Institute, Cambridge, MA
Robert Kottwitz University of Chicago, Chicago, IL
A co-publication of the AMS and Clay Mathematics Institute
Softcover ISBN:  978-0-8218-3844-0
Product Code:  CMIP/4
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
  • Book Details
     
     
    Clay Mathematics Proceedings
    Volume: 42005; 689 pp
    MSC: Primary 11; Secondary 14; 22;

    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).

    Readership

    Graduate students and research mathematicians interested in number theory, automorphic forms, and group representations.

  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 42005; 689 pp
MSC: Primary 11; Secondary 14; 22;

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).

Readership

Graduate students and research mathematicians interested in number theory, automorphic forms, and group representations.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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