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Author  Title  Accn#  Year  Item Type  Claims 
1 
SchulzBaldes, Hermann 
Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems 
I12255 
2022 
Book 

2 
Prodan, Emil 
A Computational Noncommutative Geometry Program for Disordered Topological Insulators 
I10352 
2017 
eBook 

3 
Prodan, Emil 
Bulk and Boundary Invariants for Complex Topological Insulators 
I10122 
2016 
eBook 

4 
Gordon, B. Brent 
The Arithmetic and Geometry of Algebraic Cycles 
I10736 
2000 
eBook 

5 
Jardine, John F 
Algebraic KTheory: Connections with Geometry and Topology 
I03578 
1989 
eBook 

6 
Goerss, P.G 
Algebraic KTheory and Algebraic Topology 
I02299 
1993 
eBook 

7 
Alain Connes 
Noncommutative geometry 
018342 
1994 
Book 


1.


Title  Harmonic Analysis in Operator Algebras and its Applications to Index Theory and Topological Solid State Systems 
Author(s)  SchulzBaldes, Hermann;Stoiber, Tom 
Publication  Cham, 1. Imprint: Springer
2. Springer International Publishing, 2022. 
Description  XXIV, 206 p. 7 illus : online resource 
Abstract Note  This book contains a selfconsistent treatment of Besov spaces for W*dynamical systems, based on the Arveson spectrum and Fourier multipliers. Generalizing classical results by Peller, spaces of Besov operators are then characterized by trace class properties of the associated Hankel operators lying in the W*crossed product algebra. These criteria allow to extend index theorems to such operator classes. This in turn is of great relevance for applications in solidstate physics, in particular, Anderson localized topological insulators as well as topological semimetals. The book also contains a selfcontained chapter on duality theory for Ractions. It allows to prove a bulkboundary correspondence for boundaries with irrational angles which implies the existence of flat bands of edge states in graphenelike systems. This book is intended for advanced students in mathematical physics and researchers alike 
ISBN,Price  9783031122019 
Keyword(s)  1. ALGEBRA
2. CONDENSED MATTER
3. CONDENSED MATTER PHYSICS
4. EBOOK
5. EBOOK  SPRINGER
6. GROUP THEORY
7. Group Theory and Generalizations
8. KTHEORY

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2.


Title  A Computational Noncommutative Geometry Program for Disordered Topological Insulators 
Author(s)  Prodan, Emil 
Publication  Cham, Springer International Publishing, 2017. 
Description  X, 118 p. 19 illus. in color : online resource 
Abstract Note  This work presents a computational program based on the principles of noncommutative 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 noncommutative 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 finitevolume approximation of the noncommutative 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 canonicalfinite 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,Price  9783319550237 
Keyword(s)  1. CONDENSED MATTER
2. CONDENSED MATTER PHYSICS
3. EBOOK
4. EBOOK  SPRINGER
5. FUNCTIONAL ANALYSIS
6. KTHEORY
7. Mathematical Methods in Physics
8. MATHEMATICAL PHYSICS
9. PHYSICS

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I10352 


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3.


Title  Bulk and Boundary Invariants for Complex Topological Insulators : From KTheory to Physics 
Author(s)  Prodan, Emil;SchulzBaldes, Hermann 
Publication  Cham, Springer International Publishing, 2016. 
Description  XXII, 204 p. 1 illus : online resource 
Abstract Note  This 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 Ktheory and noncommutative 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 nontrivial 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,Price  9783319293516 
Keyword(s)  1. EBOOK
2. EBOOK  SPRINGER
3. KTHEORY
4. Mathematical Methods in Physics
5. MATHEMATICAL PHYSICS
6. PHYSICS
7. SOLID STATE PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I10122 


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4.


Title  The Arithmetic and Geometry of Algebraic Cycles 
Author(s)  Gordon, B. Brent;Lewis, James D;M??llerStach, Stefan;Saito, Shuji;Yui, Noriko 
Publication  Dordrecht, Springer Netherlands, 2000. 
Description  XXX, 615 p : online resource 
Abstract Note  The 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 kickoff activity of the CRM 199899 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,Price  9789401140980 
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. KTHEORY
13. Manifolds (Mathematics)

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Call#  Status  Issued To  Return Due On  Physical Location 
I10736 


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5.


Title  Algebraic KTheory: Connections with Geometry and Topology 
Author(s)  Jardine, John F;Snaith, V.P 
Publication  Dordrecht, Springer Netherlands, 1989. 
Description  XIV, 550 p : online resource 
Abstract Note  A NATO Advanced Study Institute entitled "Algebraic Ktheory: 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 Ktheory 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 wellknown list of 1973, as well as a short list of new problems 
ISBN,Price  9789400923997 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. ALGEBRAIC TOPOLOGY
3. EBOOK
4. EBOOK  SPRINGER
5. KTHEORY

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Call#  Status  Issued To  Return Due On  Physical Location 
I03578 


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6.


Title  Algebraic KTheory and Algebraic Topology 
Author(s)  Goerss, P.G;Jardine, John F 
Publication  Dordrecht, Springer Netherlands, 1993. 
Description  XII, 328 p : online resource 
Abstract Note  A NATO Advanced Study Institute entitled "Algebraic Ktheory 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 Ktheoretic art at the end of 1991. The underlying objective of the meeting was to discuss recent work related to the LichtenbaumQuillen 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,Price  9789401706957 
Keyword(s)  1. ALGEBRA
2. ALGEBRAIC GEOMETRY
3. ALGEBRAIC TOPOLOGY
4. Associative rings
5. Associative Rings and Algebras
6. EBOOK
7. EBOOK  SPRINGER
8. KTHEORY
9. Order, Lattices, Ordered Algebraic Structures
10. Ordered algebraic structures
11. Rings (Algebra)

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Call#  Status  Issued To  Return Due On  Physical Location 
I02299 


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