A Course On Holomorphic Discs

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A Course On Holomorphic Discs

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Author : Hansjörg Geiges
language : en
Publisher:
Release Date : 2023

A Course On Holomorphic Discs written by Hansjörg Geiges and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with categories.

This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov's nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology. This text can be used as the basis for a graduate course, and it is also immensely suitable for independent study. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed. This book is also part of the Virtual Series on Symplectic Geometry.

A Course On Holomorphic Discs

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Author : Hansjörg Geiges
language : en
Publisher: Springer Nature
Release Date : 2023-08-07

A Course On Holomorphic Discs written by Hansjörg Geiges and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-07 with Mathematics categories.

This textbook, based on a one-semester course taught several times by the authors, provides a self-contained, comprehensive yet concise introduction to the theory of pseudoholomorphic curves. Gromov’s nonsqueezing theorem in symplectic topology is taken as a motivating example, and a complete proof using pseudoholomorphic discs is presented. A sketch of the proof is discussed in the first chapter, with succeeding chapters guiding the reader through the details of the mathematical methods required to establish compactness, regularity, and transversality results. Concrete examples illustrate many of the more complicated concepts, and well over 100 exercises are distributed throughout the text. This approach helps the reader to gain a thorough understanding of the powerful analytical tools needed for the study of more advanced topics in symplectic topology. /divThis text can be used as the basis for a graduate course, and it is also immensely suitable for independent study. Prerequisites include complex analysis, differential topology, and basic linear functional analysis; no prior knowledge of symplectic geometry is assumed. This book is also part of the Virtual Series on Symplectic Geometry.

A Course In Complex Analysis

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Author : Saeed Zakeri
language : en
Publisher: Princeton University Press
Release Date : 2021-11-02

A Course In Complex Analysis written by Saeed Zakeri and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-02 with Mathematics categories.

"This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--

A Course In Complex Analysis In One Variable

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Author : Moskowitz Martin
language : en
Publisher: World Scientific Publishing Company
Release Date : 2002-04-17

A Course In Complex Analysis In One Variable written by Moskowitz Martin and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-17 with Mathematics categories.

Complex analysis is a beautiful subject — perhaps the single most beautiful; and striking; in mathematics. It presents completely unforeseen results that are of a dramatic; even magical; nature. This invaluable book will convey to the student its excitement and extraordinary character. The exposition is organized in an especially efficient manner; presenting basic complex analysis in around 130 pages; with about 50 exercises. The material constantly relates to and contrasts with that of its sister subject; real analysis. An unusual feature of this book is a short final chapter containing applications of complex analysis to Lie theory.Since much of the content originated in a one-semester course given at the CUNY Graduate Center; the text will be very suitable for first year graduate students in mathematics who want to learn the basics of this important subject. For advanced undergraduates; there is enough material for a year-long course or; by concentrating on the first three chapters; for one-semester course.

Holomorphic Curves In Symplectic Geometry

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Author : Michele Audin
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Holomorphic Curves In Symplectic Geometry written by Michele Audin and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is devoted to pseudo-holomorphic curve methods in symplectic geometry. It contains an introduction to symplectic geometry and relevant techniques of Riemannian geometry, proofs of Gromov's compactness theorem, an investigation of local properties of holomorphic curves, including positivity of intersections, and applications to Lagrangian embeddings problems. The chapters are based on a series of lectures given previously by the authors M. Audin, A. Banyaga, P. Gauduchon, F. Labourie, J. Lafontaine, F. Lalonde, Gang Liu, D. McDuff, M.-P. Muller, P. Pansu, L. Polterovich, J.C. Sikorav. In an attempt to make this book accessible also to graduate students, the authors provide the necessary examples and techniques needed to understand the applications of the theory. The exposition is essentially self-contained and includes numerous exercises.

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Author :
language : en
Publisher:
Release Date : 1781

written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1781 with categories.

Holomorphic Dynamical Systems

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Author : Nessim Sibony
language : en
Publisher: Springer
Release Date : 2010-07-20

Holomorphic Dynamical Systems written by Nessim Sibony and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-20 with Mathematics categories.

The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.

Topics In Singularity Theory

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Author : Alekseĭ Nikolaevich Khovanskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Topics In Singularity Theory written by Alekseĭ Nikolaevich Khovanskiĭ 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 1997 with Geometry, Projective categories.

Quantum Fields And Strings A Course For Mathematicians

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Author : Pierre Deligne
language : en
Publisher: American Mathematical Society
Release Date : 2000-04-27

Quantum Fields And Strings A Course For Mathematicians written by Pierre Deligne and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-27 with Mathematics categories.

A run-away bestseller from the moment it hit the market in late 1999. This impressive, thick softcover offers mathematicians and mathematical physicists the opportunity to learn about the beautiful and difficult subjects of quantum field theory and string theory. Cover features an intriguing cartoon that will bring a smile to its intended audience.

Complex Geometry

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Author : Daniel Huybrechts
language : en
Publisher: Springer Science & Business Media
Release Date : 2005

Complex Geometry written by Daniel Huybrechts 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 2005 with Computers categories.

Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)