Isomonodromic deformations and frobenius manifolds: an introduction

Based on a series of graduate lectures, this book provides an introduction toalgebraic 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 theirdeformations, 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. First book to cover this material at a level that is accessible to graduate students and young researchers.Includes complete proofs, and applications to recent research questions INDICE: The language of fibre bundles. Holomorphic vector bundles on the Riemann sphere. The Riemann-Hilbert correspondence. Lattices. The Riemann-Hilbert problem and Birkhoff's problem. Fourier-Laplace duality. Integrable deformations. Saito structures and Frobenius structures. References. Index of notation. Index.

• ISBN: 978-1-84800-053-7
• Editorial: Springer
• Encuadernacion: Rústica
• Páginas: 305
• Fecha Publicación: 01/01/2008
• Nº Volúmenes: 1
• Idioma: Inglés