This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session. Key topics are moduli spaces of points on P1 and Picard-Terada-Deligne-Mostow theory, moduli spaces of K3 surfaces, complex hyperbolic geometry, ball quotients, GKZ hypergeometric structures, Hilbert and Picard modular surfaces, uniformizations of complex orbifolds, algebraicity of values of Schwartz triangle functions, and Thakur's hypergeometric function. The book provides a background, gives detailed expositions and indicates new research directions. It is directed to postgraduate students and researchers.

Presents reviewed and polished lecture notes, survey articles and original research results written by acknowledged experts in the field Contains a stimulating collection of open problems

Zusammenfassung

This volume comprises lecture notes, survey and research articles originating from the CIMPA Summer School Arithmetic and Geometry around Hypergeometric Functions held at Galatasaray University, Istanbul, June 13-25, 2005. It covers a wide range of topics related to hypergeometric functions, thus giving a broad perspective of the state of the art in the field.

Inhalt
Hyperbolic Geometry and the Moduli Space of Real Binary Sextics.- Gauss' Hypergeometric Function.- Moduli of K3 Surfaces and Complex Ball Quotients.- Macbeaths infinite series of Hurwitz groups.- Relative Proportionality on Picard and Hilbert Modular Surfaces.- Hypergeometric Functions and Carlitz Differential Equations over Function Fields.- The Moduli Space of 5 Points on ?1 and K3 Surfaces.- Uniformization by Lauricella Functions An Overview of the Theory of Deligne-Mostow.- Invariant Functions with Respect to the Whitehead-Link.- On the Construction of Class Fields by Picard Modular Forms.- Algebraic Values of Schwarz Triangle Functions.- GKZ Hypergeometric Structures.- Orbifolds and Their Uniformization.- From the Power Function to the Hypergeometric Function.- Problem Session.