Computational Approach To Riemann Surfaces

Author : Alexander I. Bobenko TU Berlin,Christian Klein
Publisher : Springer
Page : 264 pages
File Size : 44,5 Mb
Release : 2011-02-03
Category : Mathematics
ISBN : 9783642174131

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Computational Approach to Riemann Surfaces by Alexander I. Bobenko TU Berlin,Christian Klein Pdf

This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Author : Alexander I. Bobenko,Christian Klein
Publisher : Unknown
Page : 278 pages
File Size : 46,8 Mb
Release : 2011-03-30
Category : Electronic
ISBN : 3642174140

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Computational Approach to Riemann Surfaces by Alexander I. Bobenko,Christian Klein Pdf

Author : Alexander I. Bobenko
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 52,7 Mb
Release : 2011-02-12
Category : Mathematics
ISBN : 9783642174124

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Computational Approach to Riemann Surfaces by Alexander I. Bobenko Pdf

This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.

Author : Terrence Napier,Mohan Ramachandran
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 44,7 Mb
Release : 2011-09-08
Category : Mathematics
ISBN : 9780817646936

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An Introduction to Riemann Surfaces by Terrence Napier,Mohan Ramachandran Pdf

This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method. This method is a powerful technique from the theory of several complex variables, and provides for a unique approach to the fundamentally different characteristics of compact and noncompact Riemann surfaces. The inclusion of continuing exercises running throughout the book, which lead to generalizations of the main theorems, as well as the exercises included in each chapter make this text ideal for a one- or two-semester graduate course.

Author : Lars Valerian Ahlfors,E. Calabi,Marston Morse,Leo Sario,Donald Clayton Spencer
Publisher : Princeton University Press
Page : 275 pages
File Size : 49,5 Mb
Release : 1953-08-21
Category : Mathematics
ISBN : 9780691079394

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Contributions to the Theory of Riemann Surfaces by Lars Valerian Ahlfors,E. Calabi,Marston Morse,Leo Sario,Donald Clayton Spencer Pdf

A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

Author : Robert D.M. Accola
Publisher : Springer
Page : 117 pages
File Size : 42,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540490562

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Topics in the Theory of Riemann Surfaces by Robert D.M. Accola Pdf

The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.

Author : Andrei Bogatyrev
Publisher : Springer
Page : 150 pages
File Size : 46,8 Mb
Release : 2013-01-02
Category : Mathematics
ISBN : 364225635X

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Extremal Polynomials and Riemann Surfaces by Andrei Bogatyrev Pdf

The problems of conditional optimization of the uniform (or C-) norm for polynomials and rational functions arise in various branches of science and technology. Their numerical solution is notoriously difficult in case of high degree functions. The book develops the classical Chebyshev's approach which gives analytical representation for the solution in terms of Riemann surfaces. The techniques born in the remote (at the first glance) branches of mathematics such as complex analysis, Riemann surfaces and Teichmüller theory, foliations, braids, topology are applied to approximation problems. The key feature of this book is the usage of beautiful ideas of contemporary mathematics for the solution of applied problems and their effective numerical realization. This is one of the few books where the computational aspects of the higher genus Riemann surfaces are illuminated. Effective work with the moduli spaces of algebraic curves provides wide opportunities for numerical experiments in mathematics and theoretical physics.​

Author : R. Narasimhan
Publisher : Birkhäuser
Page : 127 pages
File Size : 44,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886178

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Compact Riemann Surfaces by R. Narasimhan Pdf

Author : William A. Stein
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 41,7 Mb
Release : 2007-02-13
Category : Mathematics
ISBN : 9780821839607

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Modular Forms, a Computational Approach by William A. Stein Pdf

This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.

Author : Paraskevas Alvanos
Publisher : Walter de Gruyter GmbH & Co KG
Page : 151 pages
File Size : 41,8 Mb
Release : 2016-07-25
Category : Mathematics
ISBN : 9783110439489

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Riemann-Roch Spaces and Computation by Paraskevas Alvanos Pdf

The book focuses on the educational perspective of Riemann-Roch spaces and the computation of algebraic structures connected to the Riemann-Roch theorem, which is a useful tool in fields of complex analysis and algebraic geometry. On one hand, the theorem connects the Riemann surface with its topological genus, and on the other it allows us to compute the algebraic function field spaces. In the first part of this book, algebraic structures and some of their properties are presented. The second part shows efficient algorithms and examples connected to Riemann-Roch spaces. What is important, a variety of examples with codes of algorithms are given in the book, covering the majority of the cases.

Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 293 pages
File Size : 44,9 Mb
Release : 2006-12-13
Category : Mathematics
ISBN : 9783540330677

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Compact Riemann Surfaces by Jürgen Jost Pdf

This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.

Author : Robert C. Gunning
Publisher : Springer Science & Business Media
Page : 177 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642663826

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Riemann Surfaces and Generalized Theta Functions by Robert C. Gunning Pdf

The investigation of the relationships between compact Riemann surfaces (al gebraic curves) and their associated complex tori (Jacobi varieties) has long been basic to the study both of Riemann surfaces and of complex tori. A Riemann surface is naturally imbedded as an analytic submanifold in its associated torus; and various spaces of linear equivalence elasses of divisors on the surface (or equivalently spaces of analytic equivalence elasses of complex line bundies over the surface), elassified according to the dimensions of the associated linear series (or the dimensions of the spaces of analytic cross-sections), are naturally realized as analytic subvarieties of the associated torus. One of the most fruitful of the elassical approaches to this investigation has been by way of theta functions. The space of linear equivalence elasses of positive divisors of order g -1 on a compact connected Riemann surface M of genus g is realized by an irreducible (g -1)-dimensional analytic subvariety, an irreducible hypersurface, of the associated g-dimensional complex torus J(M); this hyper 1 surface W- r;;;, J(M) is the image of the natural mapping Mg- -+J(M), and is g 1 1 birationally equivalent to the (g -1)-fold symmetric product Mg- jSg-l of the Riemann surface M.

Author : Emilio Bujalance,Emilio Bujalance García,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 53,7 Mb
Release : 2010-10-06
Category : Mathematics
ISBN : 9783642148279

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Symmetries of Compact Riemann Surfaces by Emilio Bujalance,Emilio Bujalance García,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki Pdf

This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.

Author : Lars Valerian Ahlfors,Leo Sario
Publisher : Princeton University Press
Page : 397 pages
File Size : 42,9 Mb
Release : 2015-12-08
Category : Mathematics
ISBN : 9781400874538

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Riemann Surfaces by Lars Valerian Ahlfors,Leo Sario Pdf

The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Kichoon Yang
Publisher : World Scientific
Page : 184 pages
File Size : 46,9 Mb
Release : 1988-11-01
Category : Mathematics
ISBN : 9789814520034

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Compact Riemann Surfaces and Algebraic Curves by Kichoon Yang Pdf

This volume is an introduction to the theory of Compact Riemann Surfaces and algebraic curves. It gives a concise account of the elementary aspects of different viewpoints in curve theory. Foundational results on divisors and compact Riemann surfaces are also stated and proved. Contents:Topological Preliminaries —Singular Homology and Relative HomologyCellular HomologyDe Rham CohomologyCommutative Algebra — An Introduction —Closed Ideals and VarietiesCoordinate RingsDimension TheoryIntersection NumbersSingular Plane Curves —The Classical Plücker FormulaeDivisors on a Compact Complex Manifold —Divisors and Holomorphic Line BundlesLinear Systems on a Compact Riemann Surface and Holomorphic MapsCompact Riemann Surfaces —The Jacobian Variety and Abel's TheoremThe Riemann-Roch Theorem and the Canonical EmbeddingHyperelliptic Riemann Surfaces and the Weierstrass PointsGeometry of Projective Curves — The Complex Flag ManifoldMetric Geometry of Projective CurvesPlücker Formulae for Projective Algebraic CurvesHarmonic Maps from a Compact Riemann SurfaceA Brief Look at Algebraic Surfaces —The Intersection FormBlow-Ups and Rational MapsThe Kodaira Dimension of an Algebraic Surface Readership: Mathematicians. Keywords:Compact Riemann Surfaces;Algebraic Curves;Compact Complex Manifold;Algebraic Surfaces