Math Matiques 2e Ann E

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Hodge Theory And Complex Algebraic Geometry Ii Volume 2

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Author : Claire Voisin
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-03

Hodge Theory And Complex Algebraic Geometry Ii Volume 2 written by Claire Voisin and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-03 with Mathematics categories.

The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard–Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether–Lefschetz theorems, the generic triviality of the Abel–Jacobi maps, and most importantly Nori's connectivity theorem, which generalizes the above. The last part of the book is devoted to the relationships between Hodge theory and algebraic cycles. The book concludes with the example of cycles on abelian varieties, where some results of Bloch and Beauville, for example, are expounded. The text is complemented by exercises giving useful results in complex algebraic geometry. It will be welcomed by researchers in both algebraic and differential geometry.

Homology

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Author : Saunders MacLane
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Homology written by Saunders MacLane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.

Modular Forms And Hecke Operators

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Author : A. N. Andrianov V. G. Zhuravlev
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-08-28

Modular Forms And Hecke Operators written by A. N. Andrianov V. G. Zhuravlev and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-08-28 with Mathematics categories.

The concept of Hecke operators was so simple and natural that, soon after Hecke's work, scholars made the attempt to develop a Hecke theory for modular forms, such as Siegel modular forms. As this theory developed, the Hecke operators on spaces of modular forms in several variables were found to have arithmetic meaning. Specifically, the theory provided a framework for discovering certain multiplicative properties of the number of integer representations of quadratic forms by quadratic forms. Now that the theory has matured, the time is right for this detailed and systematic exposition of its fundamental methods and results. Features: The book starts with the basics and ends with the latest results, explaining the current status of the theory of Hecke operators on spaces of holomorphic modular forms of integer and half-integer weight congruence-subgroups of integral symplectic groups. Hecke operators are considered principally as an instrument for studying the multiplicative properties of the Fourier coefficients of modular forms. It is the authors' intent that Modular Forms and Hecke Operators help attract young researchers to this beautiful and mysterious realm of number theory.

Relations And Graphs

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Author : Gunther Schmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Relations And Graphs written by Gunther Schmidt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

Relational methods can be found at various places in computer science, notably in data base theory, relational semantics of concurrency, relationaltype theory, analysis of rewriting systems, and modern programming language design. In addition, they appear in algorithms analysis and in the bulk of discrete mathematics taught to computer scientists. This book is devoted to the background of these methods. It explains how to use relational and graph-theoretic methods systematically in computer science. A powerful formal framework of relational algebra is developed with respect to applications to a diverse range of problem areas. Results are first motivated by practical examples, often visualized by both Boolean 0-1-matrices and graphs, and then derived algebraically.

Singularities In Geometry And Topology

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Author : Jean-Paul Brasselet
language : en
Publisher: World Scientific
Release Date : 2007

Singularities In Geometry And Topology written by Jean-Paul Brasselet and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology. The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

Operator Algebras And Quantum Statistical Mechanics Ii

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Author : Ola Bratteli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Operator Algebras And Quantum Statistical Mechanics Ii written by Ola Bratteli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Singularities In Geometry And Topology Proceedings Of The Trieste Singularity Summer School And Workshop

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Author : Jean-paul Brasselet
language : en
Publisher: World Scientific
Release Date : 2007-01-16

Singularities In Geometry And Topology Proceedings Of The Trieste Singularity Summer School And Workshop written by Jean-paul Brasselet and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-16 with Mathematics categories.

Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

Elliptic Hyperbolic Partial Differential Equations

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Author : Thomas H. Otway
language : en
Publisher: Springer
Release Date : 2015-07-08

Elliptic Hyperbolic Partial Differential Equations written by Thomas H. Otway and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-08 with Mathematics categories.

This text is a concise introduction to the partial differential equations which change from elliptic to hyperbolic type across a smooth hypersurface of their domain. These are becoming increasingly important in diverse sub-fields of both applied mathematics and engineering, for example: • The heating of fusion plasmas by electromagnetic waves • The behaviour of light near a caustic • Extremal surfaces in the space of special relativity • The formation of rapids; transonic and multiphase fluid flow • The dynamics of certain models for elastic structures • The shape of industrial surfaces such as windshields and airfoils • Pathologies of traffic flow • Harmonic fields in extended projective space They also arise in models for the early universe, for cosmic acceleration, and for possible violation of causality in the interiors of certain compact stars. Within the past 25 years, they have become central to the isometric embedding of Riemannian manifolds and the prescription of Gauss curvature for surfaces: topics in pure mathematics which themselves have important applications. Elliptic−Hyperbolic Partial Differential Equations is derived from a mini-course given at the ICMS Workshop on Differential Geometry and Continuum Mechanics held in Edinburgh, Scotland in June 2013. The focus on geometry in that meeting is reflected in these notes, along with the focus on quasilinear equations. In the spirit of the ICMS workshop, this course is addressed both to applied mathematicians and to mathematically-oriented engineers. The emphasis is on very recent applications and methods, the majority of which have not previously appeared in book form.

Harmonic Analysis On Semi Simple Lie Groups Ii

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Author : Garth Warner
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Harmonic Analysis On Semi Simple Lie Groups Ii written by Garth Warner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

A Functorial Model Theory

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Author : Cyrus F. Nourani
language : en
Publisher: CRC Press
Release Date : 2016-04-19

A Functorial Model Theory written by Cyrus F. Nourani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.

This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.