Perspectives on noncommutative geometry
 Responsibility
 Masoud Khalkhali, Guoliang Yu, editors.
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society ; Toronto, Canada : Fields Institute for Research in Mathematical Sciences, 2011.
 Physical description
 viii, 163 p. ; 26 cm.
 Series
 Fields Institute communications.
Access
Creators/Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references.
 Contents

 Local index theorem for projective families by M.T. Benameur and A. Gorokhovsky Type III KMS states on a class of $C^*$algebras containing $O_n$ and $\mathcal{Q}_N$ and their modular index by A. L. Carey, J. Phillips, I. F. Putnam, and A. Rennie Duality, correspondences and the Lefschetz map in equivariant KKtheory: A survey by H. Emerson Twisted spectral triples and Connes' character formula by F. Fathizadeh and M. Khalkhali Spectral morphisms, Ktheory, and stable ranks by B. Nica A survey of braided Hopf cyclic cohomology by A. Pourkia A survey of RankinCohen deformations by R. Rochberg, X. Tang, and Y.J. Yao Pseudodifferential operators and regularity of spectral triples by O. Uuye.
 (source: Nielsen Book Data)
 Publisher's Summary
 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.
(source: Nielsen Book Data)
Subjects
 Subject
 KKtheory.
 Hopf algebras.
 Algebra, Homological.
 $K$theory  Higher algebraic $K$theory  $K$theory and homology; cyclic homology and cohomology.
 Associative rings and algebras  Hopf algebras, quantum groups and related topics  Hopf algebras and their applications.
 Category theory; homological algebra  Homological algebra  Simplicial sets, simplicial objects (in a category).
Bibliographic information
 Publication date
 2011
 Series
 Fields Institute communications
 ISBN
 9780821848494 (alk. paper)
 0821848496 (alk. paper)