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Perspectives on Noncommutative Geometry (Hardcover, New ed.)
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Perspectives on Noncommutative Geometry (Hardcover, New ed.)
Series: Fields Institute Communications
Expected to ship within 12 - 19 working days
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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 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.
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