Sabbah Isomonodromic Deformations and Frobenius Manifolds

An Introduction
2008
ISBN: 978-1-84800-054-4
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 279 Seiten, eBook

Reihe: Universitext

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.

Zielgruppe

Research

Autoren/Hrsg.

Sabbah, Claude

Inhaltsverzeichnis

The 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.