Guoliang Yu – författare
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7 produkter
7 produkter
Inbunden, Engelska, 2011
1 207 kr
Skickas inom 5-8 vardagar
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.
Del 189 - Cambridge Studies in Advanced Mathematics
Higher Index Theory
Inbunden, Engelska, 2020
993 kr
Skickas inom 7-10 vardagar
Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.
Inbunden, Engelska, 2020
1 497 kr
Skickas inom 10-15 vardagar
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.
Häftad, Engelska, 2021
1 497 kr
Skickas inom 10-15 vardagar
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.
Del 278 - Operator Theory: Advances and Applications
Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology
Ronald G. Douglas Memorial Volume
Inbunden, Engelska, 2020
1 603 kr
Skickas inom 10-15 vardagar
This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology.
Del 278 - Operator Theory: Advances and Applications
Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology
Ronald G. Douglas Memorial Volume
Häftad, Engelska, 2021
1 603 kr
Skickas inom 10-15 vardagar
This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology.
Del 47 - Oberwolfach Seminars
K-Theory for Group C*-Algebras and Semigroup C*-Algebras
Häftad, Engelska, 2017
432 kr
Skickas inom 10-15 vardagar
This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.Part of the most basic structural information for such a C*-algebra is contained in its K-theory. The determination of the K-groups of C*-algebras constructed from group or semigroup actions is a particularly challenging problem. Paul Baum and Alain Connes proposed a formula for the K-theory of the reduced crossed product for a group action that would permit, in principle, its computation. By work of many hands, the formula has by now been verified for very large classes of groups and this work has led to the development of a host of new techniques. An important ingredient is Kasparov's bivariant K-theory.More recently, also the C*-algebras generated by the regular representation of a semigroup as well as the crossed products for actions of semigroups by endomorphisms have been studied in more detail. Intriguing examples of actions of such semigroups come from ergodic theory as well as from algebraic number theory. The computation of the K-theory of the corresponding crossed products needs new techniques. In cases of interest the K-theory of the algebras reflects ergodic theoretic or number theoretic properties of the action.