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Book DetailsFields Institute CommunicationsVolume: 61; 2011; 163 ppMSC: 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 longstanding conjectures, such as the Novikov conjecture and the BaumConnes 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.ReadershipGraduate students and research mathematicians interested in noncommutative geometry.

Table of Contents

Chapters

MoulayTahar 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 KKtheory: A survey

Farzad Fathizadeh and Masoud Khalkhali  Twisted spectral triples and Connes’ character formula

Bogdan Nica  Spectral morphisms, Ktheory, and stable ranks

Arash Pourkia  A survey of braided Hopf cyclic cohomology

Richard Rochberg, Xiang Tang and Yijun Yao  A survey of RankinCohen deformations

Otgonbayar Uuye  Pseudodifferential operators and regularity of spectral triples


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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 longstanding conjectures, such as the Novikov conjecture and the BaumConnes 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.
Graduate students and research mathematicians interested in noncommutative geometry.

Chapters

MoulayTahar 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 KKtheory: A survey

Farzad Fathizadeh and Masoud Khalkhali  Twisted spectral triples and Connes’ character formula

Bogdan Nica  Spectral morphisms, Ktheory, and stable ranks

Arash Pourkia  A survey of braided Hopf cyclic cohomology

Richard Rochberg, Xiang Tang and Yijun Yao  A survey of RankinCohen deformations

Otgonbayar Uuye  Pseudodifferential operators and regularity of spectral triples