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Redaktion: Caterina Consani, Matilde Marcolli
Noncommutative Geometry and Number Theory
Where Arithmetic meets Geometry and Physics
erschienen April 2006
372 Seiten, Gebunden
Vieweg+Teubner Verlag | ISBN: 3834801704
| |  | 79.95 EUR |  | | |
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Preface 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 fields has now reached an important 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 possibl...
[weiter lesen]
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Caterina Consani Matilde Marcolli (Eds.) Noncommutative Geometry and Number Theory Where Arithmetic meets Geometry and Physics In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number th... [weiter lesen] |
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| INHALTSVERZEICHNIS | öffnen |
Contents
PrefaceV
The Hecke algebra of a reductive p-adic group: a view from noncommutative geometry
ANNE-MARIE AUBERT, PAUL BAUM, ROGER PLYMEN 1
Hubert modular forms and the Ramanujan conjecture
DON BLASIUS 35
Farey fractions and two-dimensional tori
FLORIN P. BOCA AND ALEXANDRU ZAHARESCU 57
Transgression of the Godbillon-Vey class and Rademacher functions
ALAIN CONNES AND HENRI MOSCOVICI 79
Archimedean cohomology revisited
CATERINA CONSANI AND MATILDE MARCOLLI 109
A twisted Burnside theorem for countable groups and Reidemeister numbers
ALEXANDER FEL'SHTYN AND EVGENIJ TROITSKY 141
Introduction to Hopf cyclic cohomology
MASOUD KHALKHALI AND BAHRAN RANGIPOUR 155
The non-abelian (or non-linear) method of Chabauty
MINHYONG KIM 179
The residues of quantum field theory - numbers we should know
DIRK KREIMER 187
Phase transitions with spontaneous symmetry breaking on Hecke C*-algebras from number...
MARCELO LACA AND MACHIEL VAN FRANKENHUIJSEN 205
On harmonic maps in noncommutative geometry
GIOVANNI LANDI 217
Towards the fractional quantum Hall effect: a noncommutative geometry perspective
MATILDE MARCOLLI AND VARGHESE MATHAI 235
Homological algebra for Schwartz algebras of reductive p-adic groups
RALPH MEYER 263
A non-commutative geometry approach to the representation theory of reductive p-adic ...
VICTOR NISTOR 301
Three examples of non-commutative boundaries of Shimura varieties
FREDERIC PAUGAM 323
Holomorphic bundles on 2-dimensional noncommutative toric orbifolds
ALEXANDER POLISHCHUK 341
A new short proof of the local index formula of Atiyah-Singer
RAPHAEL PONGE 361
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