Advances in Noncommutative Geometry

On the Occasion of Alain Connes' 70th Birthday

  • Ali Chamseddine
  • Caterina Consani
  • Nigel Higson
  • Masoud Khalkhali
  • Henri Moscovici
  • Guoliang Yu

Table of contents

  1. Front Matter
    Pages i-vii
  2. Ali Chamseddine, Walter D. van Suijlekom
    Pages 1-51
  3. Alain Connes, Caterina Consani
    Pages 53-125
  4. Maria Paula Gomez Aparicio, Pierre Julg, Alain Valette
    Pages 127-244
  5. Claire Debord, Georges Skandalis
    Pages 245-289
  6. Bjørn Ian Dundas
    Pages 291-319
  7. Farzad Fathizadeh, Masoud Khalkhali
    Pages 321-420
  8. Alexander Gorokhovsky, Erik Van Erp
    Pages 421-462
  9. Matthias Lesch, Henri Moscovici
    Pages 463-490
  10. Steven Lord, Fedor A. Sukochev, Dmitriy Zanin
    Pages 491-583
  11. Dan-Virgil Voiculescu
    Pages 585-606
  12. Raimar Wulkenhaar
    Pages 607-690
  13. Zhizhang Xie, Guoliang Yu
    Pages 691-751

About this book


This authoritative volume in honor of  Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23–April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.


Cyclic Cohomology Spectral Triples K-Theory Index Theory Geometric Analysis Riemann Hypothesis Arithmetic Algebraic Geometry Riemann-Roch strategy Alain Connes 70th birthday Baum-Connes conjecture Lie groupoids non-commutative geometry spectral geometry Gaussian curvature Dixmier traces quantum field theory

Editors and affiliations

  • Ali Chamseddine
    • 1
  • Caterina Consani
    • 2
  • Nigel Higson
    • 3
  • Masoud Khalkhali
    • 4
  • Henri Moscovici
    • 5
  • Guoliang Yu
    • 6
  1. 1.Department of Physics Institute for MathematicsAstrophysics and Particle PhysicsNijmegenThe Netherlands
  2. 2.Department of MathematicsJohns Hopkins UniversityBaltimoreUSA
  3. 3.Department of MathematicsPennsylvania State UniversityUniversity ParkUSA
  4. 4.Department of MathematicsThe University of Western OntarioLondonCanada
  5. 5.Department of MathematicsOhio State UniversityColumbusUSA
  6. 6.Department of MathematicsTexas A&M UniversityCollege StationUSA

Bibliographic information