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.

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.

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

Inhalt
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.