Perspectives on Noncommutative Geometry (Fields Institute Communications) - Hardcover

Hardcover

ISBN 10: 0821848496 ISBN 13: 9780821848494

Publisher: American Mathematical Society, 2011

Synopsis

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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2011
• Language: English
• ISBN 10: 0821848496
• ISBN 13: 9780821848494
• Binding: Hardcover
• Number of pages: 163
• Editor: Khalkhali Masoud, Yu Guoliang