Linear meromorphic differential equations: A modern point of view

Abstract

A large part of the modern theory of differential equations in the complex domain is concerned with regular singularities and holonomic systems. However the theory of differential equations with irregular singularities has a long history and has become very active in recent years. Substantial links of this theory to the theory of algebraic groups, commutative algebra, resurgent functions, and Galois differential methods have been discovered. This survey attempts a general introduction to some of these aspects, with emphasis on reduction theory, asymptotic analysis, Stokes phenomena, and certain moduli problems.