
Table of Contents 
Fields Institute Communications 2011; 163 pp; hardcover Volume: 61 ISBN10: 0821848496 ISBN13: 9780821848494 List Price: US$89 Member Price: US$71.20 Order Code: FIC/61 See also: Noncommutative Geometry, Quantum Fields and Motives  Alain Connes and Matilde Marcolli Arithmetic Noncommutative Geometry  Matilde Marcolli  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. Titles in this series are copublished with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada). Readership Graduate students and research mathematicians interested in noncommutative geometry. 


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