Quanta of Maths: Conference in honor of Alain Connes, Non Commutative Geometry, Paris, 1997

695 Pages·2010·1.91 MB·English

by  Etienne Blanchard

Clay Mathematics Proceedings
Volume 11
Quanta of Maths
Conference in honor of Alain Connes
Non Commutative Geometry
Institut Henri Poincaré, Institut des Hautes Études Scienti(cid:197) ques,
Institut de Mathématiques de Jussieu, Paris, France
March 29– April 6, 2007
Etienne Blanchard
David Ellwood
Masoud Khalkhali
Matilde Marcolli
Henri Moscovici
American Mathematical Society Sorin Popa
Editors
Clay Mathematics Institute
Quanta of Maths

Clay Mathematics Proceedings
Volume 11
Quanta of Maths
Conference in honor of Alain Connes
Non Commutative Geometry
Institut Henri Poincaré,
Institut des Hautes Études Scientifiques,
Institut de Mathématiques de Jussieu,
Paris, France
March 29– April 6, 2007
Etienne Blanchard
David Ellwood
Masoud Khalkhali
Matilde Marcolli
Henri Moscovici
Sorin Popa
Editors
American Mathematical Society
Clay Mathematics Institute
Photographs courtesy of Jean-Fran¸cois Dars.
2000 Mathematics Subject Classification. Primary 58B34.
Library of Congress Cataloging-in-Publication Data
Quanta of maths : non commutative geometry conference in honor of Alain Connes, March 29
to April 6, 2007, Institut Henri Poincar´e, Institut des hautes ´etudes scientifiques, Institut de
math´ematiquesdeJussieu,Paris,France/EtienneBlanchard...[etal.],editors.
p.cm. —(Claymathematicsproceedings;v.11)
Includesbibliographicalreferencesandindex.
ISBN978-0-8218-5203-3(alk.paper)
1.Noncommutativedifferentialgeometry—Congresses. I.Connes,Alain. II.Blanchard,Eti-
enne, 1968– III. Institut Henri Poincar´e. IV. Institut des hautes ´etudes scientifiques (Paris,
France) V.Institutdemath´ematiquesdeJussieu.
QA614.Q36 2011
512(cid:2).55—dc22
2010034787
Copying and reprinting. Materialinthisbookmaybereproducedbyanymeansfor edu-
cationaland scientific purposes without fee or permissionwith the exception ofreproduction by
servicesthatcollectfeesfordeliveryofdocumentsandprovidedthatthecustomaryacknowledg-
ment of the source is given. This consent does not extend to other kinds of copying for general
distribution, for advertising or promotional purposes, or for resale. Requests for permission for
commercialuseofmaterialshouldbeaddressedtotheAcquisitionsDepartment,AmericanMath-
ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can
[email protected].
Excludedfromtheseprovisionsismaterialinarticlesforwhichtheauthorholdscopyright. In
suchcases,requestsforpermissiontouseorreprintshouldbeaddresseddirectlytotheauthor(s).
(Copyrightownershipisindicatedinthenoticeinthelowerright-handcornerofthefirstpageof
eacharticle.)
(cid:2)c 2010bytheClayMathematicsInstitute. Allrightsreserved.
PublishedbytheAmericanMathematicalSociety,Providence,RI,
fortheClayMathematicsInstitute,Cambridge,MA.
PrintedintheUnitedStatesofAmerica.
TheClayMathematicsInstituteretainsallrights
exceptthosegrantedtotheUnitedStatesGovernment.
(cid:2)∞ Thepaperusedinthisbookisacid-freeandfallswithintheguidelines
establishedtoensurepermanenceanddurability.
VisittheAMShomepageathttp://www.ams.org/
VisittheClayMathematicsInstitutehomepageathttp://www.claymath.org/
10987654321 151413121110

Contents
Preface xi
A Geometric Description of Equivariant K-Homology for Proper Actions 1
Paul Baum, Nigel Higson and Thomas Schick
The Planar Algebra of Diagonal Subfactors 23
Dietmar Bisch, Paramita Das and Shamindra Kumar Ghosh
K -Injectivity for Properly Infinite C∗-Algebras 49
1
E´tienne Blanchard
Families of Monads and Instantons from a Noncommutative ADHM
Construction 55
Simon Brain and Giovanni Landi
Cyclic Theory for Commutative Differential Graded Algebras and
S–Cohomology 85
Dan Burghelea
Vinberg Algebras, Lie groups and Combinatorics 107
Pierre Cartier
Noncommutative Geometry as the Key to Unlock the Secrets of
Space-Time 127
Ali H. Chamseddine
The Regular C*-Algebra of an Integral Domain 149
Joachim Cuntz and Xin Li
Noncommutative Coordinate Algebras 171
Michel Dubois-Violette
Random Matrices, Free Probability, Planar Algebras and Subfactors 201
A. Guionnet, V. F. R. Jones, D. Shlyakhtenko
The Tangent Groupoid and the Index Theorem 241
Nigel Higson
Le Th´eor`eme de P´eriodicit´e en K-Th´eorie Hermitienne 257
Max Karoubi
A Short Survey of Cyclic Cohomology 283
Masoud Khalkhali
The Core Hopf Algebra 313
Dirk Kreimer
Propri´et´e (T) Renforc´ee et Conjecture de Baum-Connes 323
Vincent Lafforgue
Combinatorial Hopf algebras 347
J.-L. Loday and M. Ronco
Cyclotomy and Analytic Geometry over F 385
1
Yuri I. Manin
ix