A User's Guide to Spectral Sequences

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Author: John McCleary

Publisher: Cambridge University Press

ISBN: 9780521567596

Category: Mathematics

Page: 561

View: 4832

Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

Topology and Quantum Theory in Interaction

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Author: David Ayala,Daniel S. Freed,Ryan E. Grady

Publisher: American Mathematical Soc.

ISBN: 1470442434

Category:

Page: 258

View: 1704

This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed–Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is.

Topological Modular Forms

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Author: Christopher L. Douglas, John Francis, André G. Henriques, Michael A. Hill

Publisher: American Mathematical Soc.

ISBN: 1470418843

Category: Mathematics

Page: 318

View: 3077

The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.

Cubical Homotopy Theory

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Author: Brian A. Munson,Ismar Volić

Publisher: Cambridge University Press

ISBN: 1316351939

Category: Mathematics

Page: N.A

View: 4147

Graduate students and researchers alike will benefit from this treatment of classical and modern topics in homotopy theory of topological spaces with an emphasis on cubical diagrams. The book contains 300 examples and provides detailed explanations of many fundamental results. Part I focuses on foundational material on homotopy theory, viewed through the lens of cubical diagrams: fibrations and cofibrations, homotopy pullbacks and pushouts, and the Blakers–Massey Theorem. Part II includes a brief example-driven introduction to categories, limits and colimits, an accessible account of homotopy limits and colimits of diagrams of spaces, and a treatment of cosimplicial spaces. The book finishes with applications to some exciting new topics that use cubical diagrams: an overview of two versions of calculus of functors and an account of recent developments in the study of the topology of spaces of knots.

Introduction to Foliations and Lie Groupoids

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Author: I. Moerdijk,J. Mrcun

Publisher: Cambridge University Press

ISBN: 9781139438988

Category: Mathematics

Page: N.A

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This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.

Geometry from a Differentiable Viewpoint

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Author: John McCleary

Publisher: Cambridge University Press

ISBN: 9780521424806

Category: Mathematics

Page: 308

View: 8296

This book offers a new treatment of the topic, one which is designed to make differential geometry an approachable subject for advanced undergraduates. Professor McCleary considers the historical development of non-Euclidean geometry, placing differential geometry in the context of geometry students will be familiar with from high school. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of a particular surface, the non-Euclidean or hyperbolic plane. The main theorems of non-Euclidean geometry are presented along with their historical development. The author then introduces the methods of differential geometry and develops them toward the goal of constructing models of the hyperbolic plane. While interesting diversions are offered, such as Huygen's pendulum clock and mathematical cartography, the book thoroughly treats the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds.

Proceedings of the International Colloquium on Algebraic Groups and Homogeneous Spaces

Mumbai 2004

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Author: V. B. Mehta

Publisher: N.A

ISBN: 9788173198021

Category: Mathematics

Page: 543

View: 5807

The area of Algebraic Groups and Homogeneous Spaces is one area in which major advances have been made in recent decades. This volume contains articles by several leading experts in central topics in the area, including representation theory in characteristic p, combinatorial representation theory, flag varieties, Schubert varieties, vector bundles, loop groups and Kac-Moody Lie algebras, Galois cohomology of algebraic groups, and Tannakian categories. In addition to original papers in these areas, the volume includes a survey on representation theory in characteristic p by H. Andersen and an article by T.A. Springer on Armand Borel's work in algebraic groups and Lie groups.

Forthcoming Books

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Author: Rose Arny

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 9539

STOC '05

Proceedings of the 37th Annual ACM Symposium on Theory of Computing : Baltimore, Maryland, USA, May 22-24, 2005

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Author: N.A

Publisher: N.A

ISBN: 9781581139600

Category: Electronic digital computers

Page: 770

View: 1047

Books in Print

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5935

The Design of Everyday Things

Psychologie und Design der alltäglichen Dinge

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Author: Norman Don

Publisher: Vahlen

ISBN: 3800648105

Category: Business & Economics

Page: 320

View: 4765

Apple, Audi, Braun oder Samsung machen es vor: Gutes Design ist heute eine kritische Voraussetzung für erfolgreiche Produkte. Dieser Klassiker beschreibt die fundamentalen Prinzipien, um Dinge des täglichen Gebrauchs umzuwandeln in unterhaltsame und zufriedenstellende Produkte. Don Norman fordert ein Zusammenspiel von Mensch und Technologie mit dem Ziel, dass Designer und Produktentwickler die Bedürfnisse, Fähigkeiten und Handlungsweisen der Nutzer in den Vordergrund stellen und Designs an diesen angepasst werden. The Design of Everyday Things ist eine informative und spannende Einführung für Designer, Marketer, Produktentwickler und für alle an gutem Design interessierten Menschen. Zum Autor Don Norman ist emeritierter Professor für Kognitionswissenschaften. Er lehrte an der University of California in San Diego und der Northwest University in Illinois. Mitte der Neunzigerjahre leitete Don Norman die Advanced Technology Group bei Apple. Dort prägte er den Begriff der User Experience, um über die reine Benutzbarkeit hinaus eine ganzheitliche Erfahrung der Anwender im Umgang mit Technik in den Vordergrund zu stellen. Norman ist Mitbegründer der Beratungsfirma Nielsen Norman Group und hat unter anderem Autohersteller von BMW bis Toyota beraten. „Keiner kommt an Don Norman vorbei, wenn es um Fragen zu einem Design geht, das sich am Menschen orientiert.“ Brand Eins 7/2013 „Design ist einer der wichtigsten Wettbewerbsvorteile. Dieses Buch macht Spaß zu lesen und ist von größter Bedeutung.” Tom Peters, Co-Autor von „Auf der Suche nach Spitzenleistungen“

Algorithmen - Eine Einführung

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Author: Thomas H. Cormen,Charles E. Leiserson,Ronald Rivest,Clifford Stein

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110522012

Category: Computers

Page: 1339

View: 812

Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.