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Full Description
This authoritative volume in honor of Alain Connes, the foremost architect of Noncommutative Geometry, presents the state-of-the art in the subject. The book features an amalgam of invited survey and research papers that will no doubt be accessed, read, and referred to, for several decades to come. The pertinence and potency of new concepts and methods are concretely illustrated in each contribution. Much of the content is a direct outgrowth of the Noncommutative Geometry conference, held March 23-April 7, 2017, in Shanghai, China. The conference covered the latest research and future areas of potential exploration surrounding topology and physics, number theory, as well as index theory and its ramifications in geometry.
Contents
Foreword.- A survey of spectral models of gravity coupled to matter (Chamseddine, van Suijlekom).- The Riemann-Roch strategy, complex lift of the scaling site (Connes, Consani).- The Baum-Connes conjecture: an extended survey (Aparicio et al.).- Lie groupoids, pseudodierential calculus and index theory (Debord, Skandalis).- Cyclic homology in a special world (Dundas).- Curvature in noncommutative geometry (Fathizadeh, Khalkhali).- Index theory and noncommutative geometry: a survey (Gorokhovsky, van Erp).- Modular Gaussian curvature (Lesch, Moscovici).- Advances in Dixmier traces and applications (Lord et al.).- Commutants mod normed ideals (Voiculescu).- Quantum eld theory on noncommutative space (Wulkenhaar).- Higher invariants in noncommutative geometry (Xie, Yu).
