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基本説明
The proceedings of the Noncommutative Geometry Workshop 2008.
Full Description
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.
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 KK-theory: A survey by H. Emerson Twisted spectral triples and Connes' character formula by F. Fathizadeh and M. Khalkhali Spectral morphisms, K-theory, and stable ranks by B. Nica A survey of braided Hopf cyclic cohomology by A. Pourkia A survey of Rankin-Cohen deformations by R. Rochberg, X. Tang, and Y.-J. Yao Pseudo-differential operators and regularity of spectral triples by O. Uuye
