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1 Prodan, Emil A Computational Non-commutative Geometry Program for Disordered Topological Insulators I10352 2017 eBook  
2 Prodan, Emil Bulk and Boundary Invariants for Complex Topological Insulators I10122 2016 eBook  
3 Gordon, B. Brent The Arithmetic and Geometry of Algebraic Cycles I10736 2000 eBook  
4 Jardine, John F Algebraic K-Theory: Connections with Geometry and Topology I03578 1989 eBook  
5 Goerss, P.G Algebraic K-Theory and Algebraic Topology I02299 1993 eBook  
6 Alain Connes Noncommutative geometry 018342 1994 Book  
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1.    
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TitleA Computational Non-commutative Geometry Program for Disordered Topological Insulators
Author(s)Prodan, Emil
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionX, 118 p. 19 illus. in color : online resource
Abstract NoteThis work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons??? dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the concept of non-commutative Brillouin torus, and a list of known formulas for various physical response functions is presented. In the second part, auxiliary algebras are introduced and a canonical finite-volume approximation of the non-commutative Brillouin torus is developed. Explicit numerical algorithms for computing generic correlation functions are discussed. In the third part upper bounds on the numerical errors are derived and it is proved that the canonical-finite volume approximation converges extremely fast to the thermodynamic limit. Convergence tests and various applications concludes the presentation. The book is intended for graduate students and researchers in numerical and mathematical physics
ISBN,Price9783319550237
Keyword(s)1. CONDENSED MATTER 2. CONDENSED MATTER PHYSICS 3. EBOOK 4. EBOOK - SPRINGER 5. FUNCTIONAL ANALYSIS 6. K-THEORY 7. Mathematical Methods in Physics 8. MATHEMATICAL PHYSICS 9. PHYSICS
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TitleBulk and Boundary Invariants for Complex Topological Insulators : From K-Theory to Physics
Author(s)Prodan, Emil;Schulz-Baldes, Hermann
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXXII, 204 p. 1 illus : online resource
Abstract NoteThis monograph offers an overview of rigorous results on fermionic topological insulators from the complex classes, namely, those without symmetries or with just a chiral symmetry. Particular focus is on the stability of the topological invariants in the presence of strong disorder, on the interplay between the bulk and boundary invariants and on their dependence on magnetic fields. The first part presents motivating examples and the conjectures put forward by the physics community, together with a brief review of the experimental achievements. The second part develops an operator algebraic approach for the study of disordered topological insulators. This leads naturally to use analysis tools from K-theory and non-commutative geometry, such as cyclic cohomology, quantized calculus with Fredholm modules and index pairings. New results include a generalized Streda formula and a proof of the delocalized nature of surface states in topological insulators with non-trivial invariants. The concluding chapter connects the invariants to measurable quantities and thus presents a refined physical characterization of the complex topological insulators. This book is intended for advanced students in mathematical physics and researchers alike
ISBN,Price9783319293516
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. K-THEORY 4. Mathematical Methods in Physics 5. MATHEMATICAL PHYSICS 6. PHYSICS 7. SOLID STATE PHYSICS
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TitleThe Arithmetic and Geometry of Algebraic Cycles
Author(s)Gordon, B. Brent;Lewis, James D;M??ller-Stach, Stefan;Saito, Shuji;Yui, Noriko
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2000.
DescriptionXXX, 615 p : online resource
Abstract NoteThe NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al?? berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Netherlands, - mania, Russia, Spain, Switzerland, the United Kingdom and the United States. During a period of two weeks, 41 invited lectures and 20 contributed lec?? tures were presented. Four lectures by invited speakers were delivered every day, followed by two sessions of contributed talks. Many informal discussions and working sessions involving small groups were organized by individual partic?? ipants. In addition, participants' reprints and preprints were displayed through?? out in a lounge next to the auditorium, which further enhanced opportunities for communication and interaction
ISBN,Price9789401140980
Keyword(s)1. ALGEBRA 2. ALGEBRAIC GEOMETRY 3. Applications of Mathematics 4. APPLIED MATHEMATICS 5. EBOOK 6. EBOOK - SPRINGER 7. ENGINEERING MATHEMATICS 8. Field theory (Physics) 9. Field Theory and Polynomials 10. GLOBAL ANALYSIS (MATHEMATICS) 11. Global Analysis and Analysis on Manifolds 12. K-THEORY 13. Manifolds (Mathematics)
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TitleAlgebraic K-Theory: Connections with Geometry and Topology
Author(s)Jardine, John F;Snaith, V.P
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1989.
DescriptionXIV, 550 p : online resource
Abstract NoteA NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; it contains a discussion of the problems from Gersten's well-known list of 1973, as well as a short list of new problems
ISBN,Price9789400923997
Keyword(s)1. ALGEBRAIC GEOMETRY 2. ALGEBRAIC TOPOLOGY 3. EBOOK 4. EBOOK - SPRINGER 5. K-THEORY
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5.     
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TitleAlgebraic K-Theory and Algebraic Topology
Author(s)Goerss, P.G;Jardine, John F
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1993.
DescriptionXII, 328 p : online resource
Abstract NoteA NATO Advanced Study Institute entitled "Algebraic K-theory and Algebraic Topology" was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991. This book is the volume of proceedings for this meeting. The papers that appear here are representative of most of the lectures that were given at the conference, and therefore present a "snapshot" of the state ofthe K-theoretic art at the end of 1991. The underlying objective of the meeting was to discuss recent work related to the Lichtenbaum-Quillen complex of conjectures, fro~ both the algebraic and topological points of view. The papers in this volume deal with a range of topics, including motivic cohomology theories, cyclic homology, intersection homology, higher class field theory, and the former telescope conjecture. This meeting was jointly funded by grants from NATO and the National Science Foun?? dation in the United States. I would like to take this opportunity to thank these agencies for their support. I would also like to thank the other members of the organizing com?? mittee, namely Paul Goerss, Bruno Kahn and Chuck Weibel, for their help in making the conference successful. This was the second NATO Advanced Study Institute to be held in this venue; the first was in 1987. The success of both conferences owes much to the professionalism and helpfulness of the administration and staff of Chateau Lake Louise
ISBN,Price9789401706957
Keyword(s)1. ALGEBRA 2. ALGEBRAIC GEOMETRY 3. ALGEBRAIC TOPOLOGY 4. Associative rings 5. Associative Rings and Algebras 6. EBOOK 7. EBOOK - SPRINGER 8. K-THEORY 9. Order, Lattices, Ordered Algebraic Structures 10. Ordered algebraic structures 11. Rings (Algebra)
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6.    
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TitleNoncommutative geometry
Author(s)Alain Connes
PublicationSan Diego, Academic press, 1994.
Description661p.
ISBN,Price012185860X : USD 81.95
Classification512.7
Keyword(s)1. CYCLIC COHOMOLOGY 2. DIFFERENTIAL GEOMETRY 3. K-THEORY 4. NONCOMMUTATIVE GEOMETRY-METRIC ASPECT 5. NONCOMMUTATIVE RINGS 6. NONCOMMUTATIVE SPACE 7. OPERATOR ALGEBRAS 8. QUANTIZED CALCULUS 9. TOPOLOGY
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018342   512.7/CON/018342  On Shelf    

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