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Universitext Ser.: Isomonodromic Deformations and Frobenius Manifolds : An Introduction by Claude Sabbah (2008, Perfect)
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About this product
Product Identifiers
PublisherSpringer London, The Limited
ISBN-101848000537
ISBN-139781848000537
eBay Product ID (ePID)64161412
Product Key Features
Number of PagesXiv, 279 Pages
Publication NameIsomonodromic Deformations and Frobenius Manifolds : an Introduction
LanguageEnglish
SubjectDifferential Equations / General, Geometry / Differential, Functional Analysis, General, Algebra / General, Geometry / Algebraic, Vector Analysis, Complex Analysis
Publication Year2008
TypeTextbook
AuthorClaude Sabbah
Subject AreaMathematics
SeriesUniversitext Ser.
FormatPerfect
Dimensions
Item Height0.2 in
Item Weight16.3 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
Dewey Edition22
Number of Volumes1 vol.
IllustratedYes
Dewey Decimal515.354
Table Of ContentThe language of fibre bundles.- Holomorphic vector bundles on the Riemann sphere.- The Riemann-Hilbert correspondence on a Riemann surface.- Lattices.- The Riemann-Hilbert problem and Birkhoff's problem.- Fourier-Laplace duality.- Integrable deformations of bundles with connection on the Riemann sphere.- Saito structures and Frobenius structures on a complex analytic manifold.
SynopsisBased on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations and ends with applications to recent research questions related to mirror symmetry. The fundamental tool used within the book is that of a vector bundle with connection. There is a detailed analysis of the singularities of such objects and of their deformations, and coverage of the techniques used in the resolution of the Riemann-Hilbert problem and Birkhoff's problem. An approach to Frobenius manifolds using isomonodromic deformations of linear differential equations is also developed. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry., The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspectives on, and revealed new links between, many apparently unrelated areas of mathematics and physics. Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations and ends with applications to recent research questions related to mirror symmetry. The fundamental tool used within the book is that of a vector bundle with connection. There is a detailed analysis of the singularities of such objects and of their deformations, and coverage of the techniques used in the resolution of the Riemann-Hilbert problem and Birkhoff's problem. An approach to Frobenius manifolds using isomonodromic deformations of linear differential equations is also developed. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry., This accessible book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations., The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the seventies in the theory of singularities of holomorphic functions. Motivated by physical considerations, further development of the theory has opened new perspectives on, and revealed new links between, many apparently unrelated areas of mathematics and physics. Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations and ends with applications to recent research questions related to mirror symmetry. The fundamental tool used within the book is that of a vector bundle with connection. There is a detailed analysis of the singularities of such objects and of their deformations, and coverage of the techniques used in the resolution of the Riemann-Hilbert problem and Birkhoff?'s problem. An approach to Frobenius manifolds using isomonodromic deformations of linear differential equations is also developed. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry., Based on a series of lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. It is the first book to cover this material at a level accessible to graduate students and young researchers. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry., Based on a series of graduate lectures, this book provides an introduction to algebraic geometric methods in the theory of complex linear differential equations. Starting from basic notions in complex algebraic geometry, it develops some of the classical problems of linear differential equations. It ends with applications to recent research questions related to mirror symmetry. The fundamental tool used is that of a vector bundle with connection. The book includes complete proofs, and applications to recent research questions. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.
LC Classification NumberQA564-609
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