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Advances in Noncommutative Geometry

On the Occasion of Alain Connes' 70th Birthday

  • Book
  • © 2019

Overview

Editors:
  1. Ali Chamseddine

    1. Department of Physics Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen, The Netherlands

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  2. Caterina Consani

    1. Department of Mathematics, Johns Hopkins University, Baltimore, USA

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  3. Nigel Higson

    1. Department of Mathematics, Pennsylvania State University, University Park, USA

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  4. Masoud Khalkhali

    1. Department of Mathematics, The University of Western Ontario, London, Canada

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  5. Henri Moscovici

    1. Department of Mathematics, Ohio State University, Columbus, USA

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  6. Guoliang Yu

    1. Department of Mathematics, Texas A&M University, College Station, USA

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  • Presents an authoritative overview of noncommutative geometry by top experts in the field

  • Topics within the general framework of noncommutative geometry range from number theory to theoretical physics

  • Survey papers enable non-experts and general math/physics readers to gain an overview of the subject

  • Presents a discussion of open problems in selected areas

  • Contributions are invited by distinguished volume editors

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-vii
    Download chapter PDF

  2. A survey of spectral models of gravity coupled to matter

    • Ali Chamseddine, Walter D. van Suijlekom
    Pages 1-51

  3. The Riemann–Roch strategy

    • Alain Connes, Caterina Consani
    Pages 53-125

  4. The Baum–Connes conjecture: an extended survey

    • Maria Paula Gomez Aparicio, Pierre Julg, Alain Valette
    Pages 127-244

  5. Lie groupoids, pseudodifferential calculus, and index theory

    • Claire Debord, Georges Skandalis
    Pages 245-289

  6. Cyclic homology in a special world

    • Bjørn Ian Dundas
    Pages 291-319

  7. Curvature in noncommutative geometry

    • Farzad Fathizadeh, Masoud Khalkhali
    Pages 321-420

  8. Index theory and noncommutative geometry: a survey

    • Alexander Gorokhovsky, Erik Van Erp
    Pages 421-462

  9. Modular Gaussian curvature

    • Matthias Lesch, Henri Moscovici
    Pages 463-490

  10. Advances in Dixmier traces and applications

    • Steven Lord, Fedor A. Sukochev, Dmitriy Zanin
    Pages 491-583

  11. Commutants mod normed ideals

    • Dan-Virgil Voiculescu
    Pages 585-606

  12. Quantum field theory on noncommutative spaces

    • Raimar Wulkenhaar
    Pages 607-690

  13. Higher invariants in noncommutative geometry

    • Zhizhang Xie, Guoliang Yu
    Pages 691-751
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Keywords

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.

Editors and Affiliations

  • Department of Physics Institute for Mathematics, Astrophysics and Particle Physics, Nijmegen, The Netherlands

    Ali Chamseddine

  • Department of Mathematics, Johns Hopkins University, Baltimore, USA

    Caterina Consani

  • Department of Mathematics, Pennsylvania State University, University Park, USA

    Nigel Higson

  • Department of Mathematics, The University of Western Ontario, London, Canada

    Masoud Khalkhali

  • Department of Mathematics, Ohio State University, Columbus, USA

    Henri Moscovici

  • Department of Mathematics, Texas A&M University, College Station, USA

    Guoliang Yu

About the editors

Ali Chamseddine is professor of physics at the American University of Beirut and the IHES. Prof. Chamseddine is known for his contributions to particle physics, general relativity, and mathematical physics. He is the recipient of the Humboldt research prize (2001), the TWAS Physics prize (2009), and the G. Bude Medal, College de France (2007).

Caterina Consani is professor of mathematics at Johns Hopkins University since 2005. Prof. Consani’s research interests include arithmetic geometry, algebraic geometry, and the connections with non-commutative geometry. She is an editorial board member of the Journal of Number Theory and of Rendiconti del Seminario Matematico della Università di Padova.

Nigel Higson is Evan Pugh professor of mathematics at Penn State University. He is a specialist in noncommutative geometry. Prof. Higson was elected Fellow of the Royal Society of Canada in 2000. In 2001 he received Penn State’s Atherton Award for excellence in teaching.

Masoud Khalkhali is professor of mathematics at the University of Western Ontario and a recipient of the faculty scholar award and the graduate mentorship award. His research specialties include noncommutative geometry, mathematical physics, noncommutative spectral geometry, cyclic cohomology, quantum groups and Hopf algebras.

Henri Moscovici is professor and Alice Woods Chair in Mathematics at Ohio State University. His areas of research include noncommutative geometry, global analysis and representation theory of Lie groups.  Prof. Moscovici has received a Guggenheim Fellowship award (1995) and a Distinguished University Scholar award (2001). He was visiting professor at College de France (1986, 2004 and 2013), Sackler Scholar at Tel Aviv University (1996), Clay Mathematics Institute Scholar at Harvard University (1999), and is a Fellow of the American Mathematical Society.

Guoliang Yu is the Powell Chair in mathematics and distinguished professor of mathematics at Texas A&M University. His research interests include noncommutative geometry, K-theory of operator algebras, index theory, topology and analysis of manifolds, geometric group theory. Prof. Yu serves on the editorial board of the Journal of Topology and Analysis, Journal of Noncommutative Geometry, Annals of K-Theory, and the Kyoto Journal of Mathematics.


Bibliographic Information

  • Book Title: Advances in Noncommutative Geometry

  • Book Subtitle: On the Occasion of Alain Connes' 70th Birthday

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

  • DOI: https://doi.org/10.1007/978-3-030-29597-4

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-29596-7Published: 14 January 2020

  • Softcover ISBN: 978-3-030-29599-8Published: 26 August 2021

  • eBook ISBN: 978-3-030-29597-4Published: 13 January 2020

  • Edition Number: 1

  • Number of Pages: VII, 751

  • Number of Illustrations: 384 b/w illustrations, 18 illustrations in colour

  • Topics: Global Analysis and Analysis on Manifolds, Geometry, Number Theory

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