Noncommutative Geometry, Arithmetic, and Related Topics

Proceedings of the Twenty-First Meeting of the Japan-U.S. Mathematics Institute

Inbunden, Engelska, 2012

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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.

Produktinformation

Utgivningsdatum2012-04-11
Mått156 x 235 x 26 mm
Vikt590 g
FormatInbunden
SpråkEngelska
Antal sidor328
FörlagJohns Hopkins University Press
ISBN9781421403526

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PrefaceChapter 1. Nearby Cycles and Periodicity in Cyclic HomologyChapter 2. Modular Index Invariants of Mumford CurvesChapter 3. Characteristic 1, Entropy and the Absolute PointChapter 4. The Gauss-Bonnet Theorem for the Noncommutative Two TorusChapter 5. Zeta PhenomenologyChapter 6. Renormalization by Birkhoff-Hopf Factorization and by Generalized Evaluators: A Case StudyChapter 7. Absolute Modular FormsChapter 8. Absolute Zeta Functions and Absolute Tensor ProductsChapter 9. Mapping F1-land: An Overview of Geometries over the Field with One ElementChapter 10. Lectures on Algebraic Varieties over F1Chapter 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 Theories