Noncommutative Geometry, Arithmetic, and Related Topics

Proceedings of the Twenty-First Meeting of the Japan-U.S. Mathematics Institute
Erscheinungsjahr 2012
ISBN: 978-1-4214-0352-6
Verlag: Johns Hopkins University Press

Buch, Englisch, 328 Seiten, Format (B × H): 156 mm x 235 mm, Gewicht: 590 g

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.

Autoren/Hrsg.

Consani, Caterina

Connes, Alain

Inhaltsverzeichnis

Preface
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 Theories

Über Autor(innen)

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

Connes, Alain
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.