EDP Sciences 1775309794 20260404 fre

laboutique.edpsciences.fr-000059 03 01 01 000059 03 9782759800476 15 9782759800476 00 BA 02 1 mm 01 1 mm 08 1 gr 10 01 02 Universitext Co-édition SPRINGER-EDP Sciences sur les maths (titres de la Collection Savoirs Actuels). 01 01 Isomonodromic Deformations and Frobenius Manifolds An introduction 1 A01 01 A99 Claude Sabbah Sabbah, Claude Claude Sabbah 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) 1 01 eng 00 279 03 24 Izibook:Subject Mathématiques 24 Izibook:SubjectAndCategoryAndTags |Mathématiques| 10 2011 MAT000000 29 3052 01 510 06 05 00 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. 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 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. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry. 03 00 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. 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 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. Aimed at graduate students and researchers, the book assumes some familiarity with basic complex algebraic geometry. 02 00 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... 21 00 06 01 https://laboutique.edpsciences.fr/produit/59/9782759800476/isomonodromic-deformations-and-frobenius-manifolds 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/981/398/original/0047_couvHD.jpg 17 14 20240913T172200+0200 01 P1 EDP Sciences 01 01 P1 EDP Sciences 17 avenue du Hoggar - PA de Courtaboeuf - 91944 Les Ulis cedex A http://publications.edpsciences.org/ 04 01 00 20090101 19 00 20090101 2026 06 3052868830012 01 WORLD WORLD 08 EDP Sciences 04 01 00 20090101 03 01 D1 EDP Sciences 21 04 05 01 02 1 00 49.53 01 5.50 2.58 EUR