Baltimore, Md. : Johns Hopkins University Press, 2012. Hardcover. x,311 pp. - 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. Condition : as new copy. ISBN 9781421403526. Keywords : MATHEMATICS,

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T�tulo

Noncommutative geometry, arithmetic, and related topics.

Editor

Johns Hopkins University Press

Fecha de publicaci�n

2012

Idioma

Ingl�s

ISBN 10

1421403528

ISBN 13

9781421403526

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Encuadernaci�n de tapa dura

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as new

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Sinopsis

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.

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

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

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