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Universitext
Co-édition SPRINGER-EDP Sciences sur les maths (titres de la Collection Savoirs Actuels).
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Isomonodromic Deformations and Frobenius Manifolds
An introduction
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A99
Claude Sabbah
Sabbah, Claude
Claude
Sabbah
<p>Claude Sabbah est directeur de recherche CNRS à l'Ecole polytechnique (Palaiseau). Ses travaux portent sur les aspects algébriques des équations différentielles linéaires dans le domaine complexe, ainsi que sur leurs applications à la géométrie algébrique. (au moment de la parution de l'ouvrage)</p>
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eng
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279
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Izibook:Subject
Mathematics
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<p>The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the 1970s 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.</p> <p>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. </p> <p>The fundamental tool used within the book is that of a vector bundle with connections. 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 ismonodromics deformations of linear differential equations is also developped. </p> <p>Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.</p>
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<p>The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the 1970s 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.</p> <p>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. </p> <p>The fundamental tool used within the book is that of a vector bundle with connections. 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 ismonodromics deformations of linear differential equations is also developped. </p> <p>Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry.</p>
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The notion of a Frobenius structure on a complex analytic manifold appeared at the end of the 1970s 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 phy...
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https://laboutique.edpsciences.fr/product/59/9782759800476/isomonodromic-deformations-and-frobenius-manifolds
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