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OverviewThis 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. Full Product DetailsAuthor: Caterina Consani (The Johns Hopkins University) , Alain Connes (IHES and Vanderbilt)Publisher: Johns Hopkins University Press Imprint: Johns Hopkins University Press Dimensions: Width: 15.60cm , Height: 2.60cm , Length: 23.50cm Weight: 0.590kg ISBN: 9781421403526ISBN 10: 1421403528 Pages: 328 Publication Date: 11 April 2012 Recommended Age: From 17 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Awaiting stock  The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsPreface Chapter 1. Nearby Cycles and Periodicity in Cyclic Homology Chapter 2. Modular Index Invariants of Mumford Curves Chapter 3. Characteristic 1, Entropy and the Absolute Point Chapter 4. The Gauss-Bonnet Theorem for the Noncommutative Two Torus Chapter 5. Zeta Phenomenology Chapter 6. Renormalization by Birkhoff-Hopf Factorization and by Generalized Evaluators: A Case Study Chapter 7. Absolute Modular Forms Chapter 8. Absolute Zeta Functions and Absolute Tensor Products Chapter 9. Mapping F1-land: An Overview of Geometries over the Field with One Element Chapter 10. Lectures on Algebraic Varieties over F1 Chapter 11. Transcendence of Values of Transcendental Functions at Algebraic Points (Inaugural Monroe H. Martin Lecture and Seminar) Chapter 12. The Hopf Algebraic Structure of Perturbative Quantum Gauge TheoriesReviewsAuthor InformationAuthor Website: http://www.math.jhu.edu/~kc/Caterina Consani is a professor in the Department of Mathematics at Johns Hopkins University. Alain Connes is a professor at the College de France, Institut des Hautes Etudes Scientifiques in Bures sur Yvette, and a distinguished professor in the Department of Mathematics at Vanderbilt University. He won the Fields Medal in 1982. Tab Content 6Author Website: http://www.math.jhu.edu/~kc/Countries AvailableAll regions |
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