Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds & Picard-Fuchs Equations

Uniformization, Riemann-Hilbert Correspondence, Calabi-Yau Manifolds & Picard-Fuchs Equations Synopsis

The uniformization theorem of Riemann surfaces is one of the most beautiful and important theorems in mathematics. Besides giving a clean classification of Riemann surfaces, its proof has motivated many new methods, such as the Riemann-Hilbert correspondence, Picard-Fuchs equations, and higher-dimensional generalizations of the uniformization theorem, which include Calabi-Yau manifolds.

This volume consists of expository papers on the four topics in its title, written by experts from around the world, and is the first to put forth a comprehensive discussion of these topics, and of the relations between them. As such, it is valuable as an introduction for beginners, and as a reference for mathematicians in general.