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Perspectives on Noncommutative Geometry
 
Edited by: Masoud Khalkhali University of Western Ontario, London, ON, Canada
Guoliang Yu Vanderbilt University, Nashville, TN
A co-publication of the AMS and Fields Institute
Front Cover for Perspectives on Noncommutative Geometry
Available Formats:
Hardcover ISBN: 978-0-8218-4849-4
Product Code: FIC/61
List Price: $100.00
MAA Member Price: $90.00
AMS Member Price: $80.00
Electronic ISBN: 978-1-4704-1782-6
Product Code: FIC/61.E
List Price: $94.00
MAA Member Price: $84.60
AMS Member Price: $75.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $150.00
MAA Member Price: $135.00
AMS Member Price: $120.00
Front Cover for Perspectives on Noncommutative Geometry
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  • Front Cover for Perspectives on Noncommutative Geometry
  • Back Cover for Perspectives on Noncommutative Geometry
Perspectives on Noncommutative Geometry
Edited by: Masoud Khalkhali University of Western Ontario, London, ON, Canada
Guoliang Yu Vanderbilt University, Nashville, TN
A co-publication of the AMS and Fields Institute
Available Formats:
Hardcover ISBN:  978-0-8218-4849-4
Product Code:  FIC/61
List Price: $100.00
MAA Member Price: $90.00
AMS Member Price: $80.00
Electronic ISBN:  978-1-4704-1782-6
Product Code:  FIC/61.E
List Price: $94.00
MAA Member Price: $84.60
AMS Member Price: $75.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $150.00
MAA Member Price: $135.00
AMS Member Price: $120.00
  • Book Details
     
     
    Fields Institute Communications
    Volume: 612011; 163 pp
    MSC: Primary 58; Secondary 19; 16; 18;

    This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008.

    Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture.

    Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples.

    Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume.

    This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.

    Readership

    Graduate students and research mathematicians interested in noncommutative geometry.

  • Table of Contents
     
     
    • Chapters
    • Moulay-Tahar Benameur and Alexander Gorokhovsky - Local index theorem for projective families
    • Alan Carey, John Phillips, Ian Putnam and Adam Rennie - Type III KMS states on a class of $C^*$-algebras containing $O_n$ and $\mathcal {Q}_N$ and their modular index
    • Heath Emerson - Duality, correspondences and the Lefschetz map in equivariant KK-theory: A survey
    • Farzad Fathizadeh and Masoud Khalkhali - Twisted spectral triples and Connes’ character formula
    • Bogdan Nica - Spectral morphisms, K-theory, and stable ranks
    • Arash Pourkia - A survey of braided Hopf cyclic cohomology
    • Richard Rochberg, Xiang Tang and Yi-jun Yao - A survey of Rankin-Cohen deformations
    • Otgonbayar Uuye - Pseudo-differential operators and regularity of spectral triples
  • Additional Material
     
     
  • Request Review Copy
Volume: 612011; 163 pp
MSC: Primary 58; Secondary 19; 16; 18;

This volume represents the proceedings of the Noncommutative Geometry Workshop that was held as part of the thematic program on operator algebras at the Fields Institute in May 2008.

Pioneered by Alain Connes starting in the late 1970s, noncommutative geometry was originally inspired by global analysis, topology, operator algebras, and quantum physics. Its main applications were to settle some long-standing conjectures, such as the Novikov conjecture and the Baum-Connes conjecture.

Next came the impact of spectral geometry and the way the spectrum of a geometric operator, like the Laplacian, holds information about the geometry and topology of a manifold, as in the celebrated Weyl law. This has now been vastly generalized through Connes' notion of spectral triples.

Finally, recent years have witnessed the impact of number theory, algebraic geometry and the theory of motives, and quantum field theory on noncommutative geometry. Almost all of these aspects are touched upon with new results in the papers of this volume.

This book is intended for graduate students and researchers in both mathematics and theoretical physics who are interested in noncommutative geometry and its applications.

Readership

Graduate students and research mathematicians interested in noncommutative geometry.

  • Chapters
  • Moulay-Tahar Benameur and Alexander Gorokhovsky - Local index theorem for projective families
  • Alan Carey, John Phillips, Ian Putnam and Adam Rennie - Type III KMS states on a class of $C^*$-algebras containing $O_n$ and $\mathcal {Q}_N$ and their modular index
  • Heath Emerson - Duality, correspondences and the Lefschetz map in equivariant KK-theory: A survey
  • Farzad Fathizadeh and Masoud Khalkhali - Twisted spectral triples and Connes’ character formula
  • Bogdan Nica - Spectral morphisms, K-theory, and stable ranks
  • Arash Pourkia - A survey of braided Hopf cyclic cohomology
  • Richard Rochberg, Xiang Tang and Yi-jun Yao - A survey of Rankin-Cohen deformations
  • Otgonbayar Uuye - Pseudo-differential operators and regularity of spectral triples
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