Alexander Barvinok's Books

A Course in Convexity

By: Alexander Barvinok

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Convexity is a simple idea that manifests itself in a surprising variety of places. This fertile field has an immensely rich structure and numerous applications. Barvinok demonstrates that simplicity, intuitive appeal, and the universality of applications make teaching (and learning) convexity a gratifying experience. The book will benefit both teacher and student: It is easy to understand, entertaining to the reader, and includes many exercises that vary in degree of difficulty. Overall, the author demonstrates the power of a few simple unifying principles in a variety of pure and applied problems. The prerequisites are minimal amounts of linear algebra, analysis, and elementary topology, plus basic computational skills. Portions of the book could be used by advanced undergraduates. As a whole, it is designed for graduate students interested in mathematical methods, computer science, electrical engineering, and operations research. The book will also be of interest to research mathematicians, who will find some results that are recent, some that are new, and many known results that are discussed from a new perspective.

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Page Count

378

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821829688

ISBN 13

9780821829684

Combinatorics and Complexity of Partition Functions

By: Alexander Barvinok

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Combinatorics and Complexity of Partition Functions

By: Alexander Barvinok

Partition functions arise in combinatorics and related problems of statistical physics as they encode in a succinct way the combinatorial structure of complicated systems. The main focus of the book is on efficient ways to compute (approximate) various partition functions, such as permanents, hafnians and their higher-dimensional versions, graph and hypergraph matching polynomials, the independence polynomial of a graph and partition functions enumerating 0-1 and integer points in polyhedra, which allows one to make algorithmic advances in otherwise intractable problems. The book unifies various, often quite recent, results scattered in the literature, concentrating on the three main approaches: scaling, interpolation and correlation decay. The prerequisites include moderate amounts of real and complex analysis and linear algebra, making the book accessible to advanced math and physics undergraduates.

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Page Count

304

Publisher

Springer

Published Date

ISBN 10

3319518291

ISBN 13

9783319518299

Integer Points in Polyhedra

By: Alexander Barvinok

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Integer Points in Polyhedra

By: Alexander Barvinok

This is a self-contained exposition of several core aspects of the theory of rational polyhedra with a view towards algorithmic applications to efficient counting of integer points, a problem arising in many areas of pure and applied mathematics. The approach is based on the consistent development and application of the apparatus of generating functions and the algebra of polyhedra. Topics range from classical, such as the Euler characteristic, continued fractions, Ehrhart polynomial, Minkowski Convex Body Theorem, and the Lenstra-Lenstra-Lovasz lattice reduction algorithm, to recent advances such as the Berline-Vergne local formula. The text is intended for graduate students and researchers. Prerequisites are a modest background in linear algebra and analysis as well as some general mathematical maturity. Numerous figures, exercises of varying degree of difficulty as well as references to the literature and publicly available software make the text suitable for a graduate course.

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Page Count

204

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190523

ISBN 13

9783037190524

History of the Byzantine Empire, 324–1453, Volume II

By: Alexander A. Vasiliev

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History of the Byzantine Empire, 324–1453, Volume II

By: Alexander A. Vasiliev

“This is the revised English translation from the original work in Russian of the history of the Great Byzantine Empire. It is the most complete and thorough work on this subject. From it we get a wonderful panorama of the events and developments of the struggles of early Christianity, both western and eastern, with all of its remains of the wonderful productions of art, architecture, and learning.”—Southwestern Journal of Theology

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Page Count

481

Publisher

Univ of Wisconsin Press

Published Date

ISBN 10

0299809269

ISBN 13

9780299809263

Discrete Differential Geometry

Integrable Structure

By: Alexander I. Bobenko,Yuri B. Suris

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Discrete Differential Geometry

Integrable Structure

By: Alexander I. Bobenko,Yuri B. Suris

An emerging field of discrete differential geometry aims at the development of discrete equivalents of notions and methods of classical differential geometry. The latter appears as a limit of a refinement of the discretization. Current interest in discrete differential geometry derives not only from its importance in pure mathematics but also from its applications in computer graphics, theoretical physics, architecture, and numerics. Rather unexpectedly, the very basic structures of discrete differential geometry turn out to be related to the theory of integrable systems. One of the main goals of this book is to reveal this integrable structure of discrete differential geometry. For a given smooth geometry one can suggest many different discretizations. Which one is the best? This book answers this question by providing fundamental discretization principles and applying them to numerous concrete problems. It turns out that intelligent theoretical discretizations are distinguished also by their good performance in applications. The intended audience of this book is threefold. It is a textbook on discrete differential geometry and integrable systems suitable for a one semester graduate course. On the other hand, it is addressed to specialists in geometry and mathematical physics. It reflects the recent progress in discrete differential geometry and contains many original results. The third group of readers at which this book is targeted is formed by specialists in geometry processing, computer graphics, architectural design, numerical simulations, and animation. They may find here answers to the question “How do we discretize differential geometry?” arising in their specific field. Prerequisites for reading this book include standard undergraduate background (calculus and linear algebra). No knowledge of differential geometry is expected, although some familiarity with curves and surfaces can be helpful.

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Page Count

432

Publisher

American Mathematical Society

Published Date

ISBN 10

1470474565

ISBN 13

9781470474560

Combinatorial Optimization

Polyhedra and Efficiency

By: Alexander Schrijver

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Combinatorial Optimization

Polyhedra and Efficiency

By: Alexander Schrijver

From the reviews: "About 30 years ago, when I was a student, the first book on combinatorial optimization came out referred to as "the Lawler" simply. I think that now, with this volume Springer has landed a coup: "The Schrijver". The box is offered for less than 90.- EURO, which to my opinion is one of the best deals after the introduction of this currency." OR-Spectrum

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Page Count

2024

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540443894

ISBN 13

9783540443896

Geometric Invariant Theory and Decorated Principal Bundles

By: Alexander H. W. Schmitt

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Geometric Invariant Theory and Decorated Principal Bundles

By: Alexander H. W. Schmitt

The book starts with an introduction to Geometric Invariant Theory (GIT). The fundamental results of Hilbert and Mumford are exposed as well as more recent topics such as the instability flag, the finiteness of the number of quotients, and the variation of quotients. In the second part, GIT is applied to solve the classification problem of decorated principal bundles on a compact Riemann surface. The solution is a quasi-projective moduli scheme which parameterizes those objects that satisfy a semistability condition originating from gauge theory. The moduli space is equipped with a generalized Hitchin map. Via the universal Kobayashi-Hitchin correspondence, these moduli spaces are related to moduli spaces of solutions of certain vortex type equations. Potential applications include the study of representation spaces of the fundamental group of compact Riemann surfaces. The book concludes with a brief discussion of generalizations of these findings to higher dimensional base varieties, positive characteristic, and parabolic bundles. The text is fairly self-contained (e.g., the necessary background from the theory of principal bundles is included) and features numerous examples and exercises. It addresses students and researchers with a working knowledge of elementary algebraic geometry.

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Page Count

404

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190655

ISBN 13

9783037190654

Combinatorics and Complexity of Partition Functions

By: Alexander Barvinok

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Combinatorics and Complexity of Partition Functions

By: Alexander Barvinok

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Page Count

304

Publisher

Springer

Published Date

ISBN 10

3319518291

ISBN 13

9783319518299

A Course in Convexity

By: Alexander Barvinok

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A Course in Convexity

By: Alexander Barvinok

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Page Count

378

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821829688

ISBN 13

9780821829684

Integer Points in Polyhedra

By: Alexander Barvinok

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Integer Points in Polyhedra

By: Alexander Barvinok

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Page Count

204

Publisher

European Mathematical Society

Published Date

ISBN 10

3037190523

ISBN 13

9783037190524

Book's by Alexander Barvinok

A Course in Convexity

A Course in Convexity

Combinatorics and Complexity of Partition Functions

Combinatorics and Complexity of Partition Functions

Integer Points in Polyhedra

Integer Points in Polyhedra

History of the Byzantine Empire, 324–1453, Volume II

History of the Byzantine Empire, 324–1453, Volume II

Discrete Differential Geometry

Discrete Differential Geometry

Combinatorial Optimization

Combinatorial Optimization

Geometric Invariant Theory and Decorated Principal Bundles

Geometric Invariant Theory and Decorated Principal Bundles

Combinatorics and Complexity of Partition Functions

Combinatorics and Complexity of Partition Functions

A Course in Convexity

A Course in Convexity

Integer Points in Polyhedra

Integer Points in Polyhedra

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