Spectral Flow

Author : T. Suslina
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 52,5 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 0821890778

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Spectral Theory of Differential Operators by T. Suslina Pdf

"This volume is dedicated to the eightieth birthday of Professor M. Sh. Birman. It contains original articles in spectral and scattering theory of differential operators, in particular, Schrodinger operators, and in homogenization theory. All articles are written by members of M. Sh. Birman's research group who are affiliated with different universities all over the world. A specific feature of the majority of the papers is a combination of traditional methods with new modern ideas."--BOOK JACKET.

Author : Nora Doll,Hermann Schulz-Baldes,Nils Waterstraat
Publisher : Walter de Gruyter GmbH & Co KG
Page : 460 pages
File Size : 45,7 Mb
Release : 2023-06-19
Category : Mathematics
ISBN : 9783111172477

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Spectral Flow by Nora Doll,Hermann Schulz-Baldes,Nils Waterstraat Pdf

Author : Natasha S. Barteneva,Ivan A. Vorobjev
Publisher : Springer Nature
Page : 265 pages
File Size : 48,5 Mb
Release : 2023-04-19
Category : Science
ISBN : 9781071630204

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Spectral and Imaging Cytometry by Natasha S. Barteneva,Ivan A. Vorobjev Pdf

This second edition volume expands on the previous edition with discussions on the latest approaches used in the spectral cytometry field. Beginning with a brief history of spectral cytometry development, this book continues with a section addressing new protocols in different areas of imaging cytometry based on the unique technology of Imagestream and also introduces FlowCam – cytometer with capabilities of analyzing phytoplankton and zooplankton. Written for the highly successful Methods in Molecular Biology series, chapters include brief introductions to their respective topics, complete lists of the materials and reagents necessary, and reproducible laboratory protocols with tips on troubleshooting and recommendations. Cutting-edge and thorough, Spectral and Imaging Flow Cytometry: Methods and Protocols, Second Edition is a valuable resources for beginners and professionals interested in learning more about this developing field. Chapters 1, 2, and 5 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Author : Marius Mantoiu,Georgi Raikov,Rafael Tiedra de Aldecoa
Publisher : Birkhäuser
Page : 255 pages
File Size : 55,9 Mb
Release : 2016-06-30
Category : Mathematics
ISBN : 9783319299921

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Spectral Theory and Mathematical Physics by Marius Mantoiu,Georgi Raikov,Rafael Tiedra de Aldecoa Pdf

The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schrödinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

Author : Nikolai Saveliev
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 47,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662047057

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Invariants of Homology 3-Spheres by Nikolai Saveliev Pdf

The book gives a systematic exposition of the diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered include: constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, and Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. The text will be a valuable source for both the graduate student and researcher in mathematics and theoretical physics.

Author : Joachim J. R. Cuntz,Masoud Khalkhali
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 51,7 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 0821871242

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Cyclic Cohomology and Noncommutative Geometry by Joachim J. R. Cuntz,Masoud Khalkhali Pdf

Noncommutative geometry is a new field that is among the great challenges of present-day mathematics. Its methods allow one to treat noncommutative algebras - such as algebras of pseudodifferential operators, group algebras, or algebras arising from quantum field theory - on the same footing as commutative algebras, that is, as spaces. Applications range over many fields of mathematics and mathematical physics. This volume contains the proceedings of the workshop on "Cyclic Cohomology and Noncommutative Geometry" held at The Fields Institute (Waterloo, ON) in June 1995. The workshop was part of the program for the special year on operator algebras and its applications.

Author : Vijay Kumar Patodi,M. S. Narasimhan
Publisher : World Scientific
Page : 318 pages
File Size : 52,5 Mb
Release : 1996
Category : Mathematics
ISBN : 9810226594

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Collected Papers of V.K. Patodi by Vijay Kumar Patodi,M. S. Narasimhan Pdf

Vijay Kumar Patodi was a brilliant Indian mathematicians who made, during his short life, fundamental contributions to the analytic proof of the index theorem and to the study of differential geometric invariants of manifolds. This set of collected papers edited by Prof M Atiyah and Prof Narasimhan includes his path-breaking papers on the McKean-Singer conjecture and the analytic proof of Riemann-Roch-Hirzebruch theorem for Kähler manifolds. It also contains his celebrated joint papers on the index theorem and the Atiyah-Patodi-Singer invariant.

Author : Alan Carey,Galina Levitina
Publisher : Springer Nature
Page : 186 pages
File Size : 47,6 Mb
Release : 2022-11-30
Category : Mathematics
ISBN : 9783031194368

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Index Theory Beyond the Fredholm Case by Alan Carey,Galina Levitina Pdf

This book is about extending index theory to some examples where non-Fredholm operators arise. It focuses on one aspect of the problem of what replaces the notion of spectral flow and the Fredholm index when the operators in question have zero in their essential spectrum. Most work in this topic stems from the so-called Witten index that is discussed at length here. The new direction described in these notes is the introduction of `spectral flow beyond the Fredholm case'. Creating a coherent picture of numerous investigations and scattered notions of the past 50 years, this work carefully introduces spectral flow, the Witten index and the spectral shift function and describes their relationship. After the introduction, Chapter 2 carefully reviews Double Operator Integrals, Chapter 3 describes the class of so-called p-relative trace class perturbations, followed by the construction of Krein's spectral shift function in Chapter 4. Chapter 5 reviews the analytic approach to spectral flow, culminating in Chapter 6 in the main abstract result of the book, namely the so-called principal trace formula. Chapter 7 completes the work with illustrations of the main results using explicit computations on two examples: the Dirac operator in Rd, and a differential operator on an interval. Throughout, attention is paid to the history of the subject and earlier references are provided accordingly. The book is aimed at experts in index theory as well as newcomers to the field.

Author : Edouard B. Sonin
Publisher : Cambridge University Press
Page : 405 pages
File Size : 45,8 Mb
Release : 2016-02-04
Category : Science
ISBN : 9781107006683

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Dynamics of Quantised Vortices in Superfluids by Edouard B. Sonin Pdf

This book draws together all the basic principles of vortex dynamics in neutral superfluids in one comprehensive volume.

Author : Michael Atiyah
Publisher : Oxford University Press
Page : 728 pages
File Size : 55,8 Mb
Release : 1988-04-28
Category : Biography & Autobiography
ISBN : 0198532792

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Michael Atiyah Collected Works by Michael Atiyah Pdf

This is a collection of the works of Michael Atiyah, a well-established mathematician and winner of the Fields Medal. It is thematically divided into volumes; this one discusses gauge theory, a current topic of research.

Author : Gerd Grubb,Krzysztof P. Wojciechowski
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 47,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821835364

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Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds by Gerd Grubb,Krzysztof P. Wojciechowski Pdf

In recent years, increasingly complex methods have been brought into play in the treatment of geometric and topological problems for partial differential operators on manifolds. This collection of papers, resulting from a Workshop on Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds, provides a broad picture of these methods with new results. Subjects in the book cover a wide variety of topics, from recent advances in index theory and the more general boundary, to applications of those invariants in geometry, topology, and physics. Papers are grouped into four parts: Part I gives an overview of the subject from various points of view. Part II deals with spectral invariants, such as geometric and topological questions. Part IV deals specifically with problems on manifolds with singularities. The book is suitable for graduate students and researchers interested in spectral problems in geometry.

Author : Jørgen E. Andersen,Jørgen Ellegaard Andersen
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 45,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853535

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Chern-Simons Gauge Theory: 20 Years After by Jørgen E. Andersen,Jørgen Ellegaard Andersen Pdf

In 1989, Edward Witten discovered a deep relationship between quantum field theory and knot theory, and this beautiful discovery created a new field of research called Chern-Simons theory. This field has the remarkable feature of intertwining a large number of diverse branches of research in mathematics and physics, among them low-dimensional topology, differential geometry, quantum algebra, functional and stochastic analysis, quantum gravity, and string theory. The 20-year anniversary of Witten's discovery provided an opportunity to bring together researchers working in Chern-Simons theory for a meeting, and the resulting conference, which took place during the summer of 2009 at the Max Planck Institute for Mathematics in Bonn, included many of the leading experts in the field. This volume documents the activities of the conference and presents several original research articles, including another monumental paper by Witten that is sure to stimulate further activity in this and related fields. This collection will provide an excellent overview of the current research directions and recent progress in Chern-Simons gauge theory.

Author : Ralph Blumenhagen,Erik Plauschinn
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 54,7 Mb
Release : 2009-07-31
Category : Science
ISBN : 9783642004490

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Introduction to Conformal Field Theory by Ralph Blumenhagen,Erik Plauschinn Pdf

Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields.

Author : Bernhelm Booß-Bavnbek,Chaofeng Zhu
Publisher : American Mathematical Soc.
Page : 123 pages
File Size : 53,5 Mb
Release : 2018-03-19
Category : Banach spaces
ISBN : 9781470428006

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The Maslov Index in Symplectic Banach Spaces by Bernhelm Booß-Bavnbek,Chaofeng Zhu Pdf

The authors consider a curve of Fredholm pairs of Lagrangian subspaces in a fixed Banach space with continuously varying weak symplectic structures. Assuming vanishing index, they obtain intrinsically a continuously varying splitting of the total Banach space into pairs of symplectic subspaces. Using such decompositions the authors define the Maslov index of the curve by symplectic reduction to the classical finite-dimensional case. The authors prove the transitivity of repeated symplectic reductions and obtain the invariance of the Maslov index under symplectic reduction while recovering all the standard properties of the Maslov index. As an application, the authors consider curves of elliptic operators which have varying principal symbol, varying maximal domain and are not necessarily of Dirac type. For this class of operator curves, the authors derive a desuspension spectral flow formula for varying well-posed boundary conditions on manifolds with boundary and obtain the splitting formula of the spectral flow on partitioned manifolds.

Author : Vladimir E. Nazaikinskii,Anton Yu. Savin,Bert-Wolfgang Schulze,Boris Yu. Sternin
Publisher : CRC Press
Page : 372 pages
File Size : 49,6 Mb
Release : 2005-08-12
Category : Mathematics
ISBN : 9781420034974

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Elliptic Theory on Singular Manifolds by Vladimir E. Nazaikinskii,Anton Yu. Savin,Bert-Wolfgang Schulze,Boris Yu. Sternin Pdf

The analysis and topology of elliptic operators on manifolds with singularities are much more complicated than in the smooth case and require completely new mathematical notions and theories. While there has recently been much progress in the field, many of these results have remained scattered in journals and preprints. Starting from an ele