Noncommutative Geometry, Arithmetic, and Related Topics: Proceedings of the Twenty-First Meeting of the Japan-U.S. Mathematics Institute

ISBN 10: 1421403528 / ISBN 13: 9781421403526

Published by Johns Hopkins University Press, 2012

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Bibliographic Details

• Title: Noncommutative Geometry, Arithmetic, and Related Topics: Proceedings of the Twenty-First Meeting of the Japan-U.S. Mathematics Institute
• Publisher: Johns Hopkins University Press
• Publication Date: 2012
• Language: English
• ISBN 10: 1421403528
• ISBN 13: 9781421403526
• Binding: Hardcover
• Condition: Like New
• Book Type: book

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Synopsis

This valuable collection of essays by some of the world’s leading scholars in mathematics presents innovative and field-defining work at the intersection of noncommutative geometry and number theory.

The interplay between these two fields centers on the study of the rich structure of the adele class space in noncommutative geometry, an important geometric space known to support and provide a geometric interpretation of the Riemann Weil explicit formulas in number theory. This space and the corresponding quantum statistical dynamical system are fundamental structures in the field of noncommutative geometry.

Several papers in this volume focus on the “field with one element” subject, a new topic in arithmetic geometry; others highlight recent developments in noncommutative geometry, illustrating unexpected connections with tropical geometry, idempotent analysis, and the theory of hyper-structures in algebra.

Originally presented at the Twenty-First Meeting of the Japan-U.S. Mathematics Institute, these essays collectively provide mathematicians and physicists with a comprehensive resource on the topic.

About the Authors

Caterina Consani is a professor in the Department of Mathematics at Johns Hopkins University.

Alain Connes is a professor at the Collège de France, Institut des Hautes Études Scientifiques in Bures sur Yvette, and a distinguished professor in the Department of Mathematics at Vanderbilt University. He won the Fields Medal in 1982.