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Noncommutative Geometry and Number Theory

Where Arithmetic meets Geometry and Physics

Caterina Consani, Matilde Marcolli (Herausgeber)

Buch | Hardcover

VIII, 372 Seiten

2006 | 2006
Vieweg & Teubner (Verlag)
978-3-8348-0170-8 (ISBN)

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In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. Research across these ?elds has now reached an imp- tant turning point, as shows the increasing interest with which the mathematical community approaches these topics. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new c- nections between the ?elds of number theory, algebraic geometry and noncom- tative geometry. Thecontributionstothisvolumepartlyre?ectthetwoworkshops“Noncom- tative Geometry and Number Theory” that took place at the Max–Planck–Institut f¨ ur Mathematik in Bonn, in August 2003 and June 2004. The two workshops were the ?rst activity entirely dedicated to the interplay between these two ?elds of mathematics. An important part of the activities, which is also re?ected in this volume, came from the hindsight of physics which often provides new perspectives onnumber theoretic problems that make it possible to employ the tools of nonc- mutative geometry, well designed to describe the quantum world.

Prof. Dr. Caterina Consani, Department of Mathematics, The Johns Hopkins University, Baltimore, USA
Prof. Dr. Matilde Marcolli, Max-Planck Institute for Mathematics, Bonn, Germany

The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Erscheint lt. Verlag	12.4.2006
Reihe/Serie	Aspects of Mathematics ; 37
Mitarbeit	Herausgeber (Serie): Klas Diederich
Zusatzinfo	VIII, 372 p.
Verlagsort	Wiesbaden
Sprache	englisch
Maße	170 x 244 mm
Gewicht	735 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Archimedean cohomology • Farey fractions • Formula of Atiyah-Singer • Fractional quantum Hall effect • Geometrie • Hecke algebra • Hopf cyclic cohomology • Method of Chabauty • Number Theory • Rademacher functions • Ramanujan conjecture • Reidemeister numbers • Schwartz algebra • Schwartz algebras • shimura varieties • Zahlentheorie
ISBN-10	3-8348-0170-4 / 3834801704
ISBN-13	978-3-8348-0170-8 / 9783834801708
Zustand	Neuware