These are lecture notes of a course given at the University of Chicago in Winter 1998. The purpose of the lectures is to give an introduction to the theory of modules over the (sheaf of) algebras of algebraic differential operators on a complex manifold. This theory was created about 1520 years ago in the works of BeilinsonBernstein and Kashiwara, and since then had a number of spectacular applications in Algebraic Geometry, Representation theory and Topology of singular spaces. We begin with defining some basic functors on Dmodules, introduce the notion of characteristic variety and of a holonomic Dmodule. We dis discuss bfunctions, and study the RiemannHilbert correspondence between holonomic Dmodules and perverse sheaves. We then go on to some deeper results about Dmodules with regular singularities. We discuss Dmodule aspects of the theory of vanishing cycles and Verdier specialization, and also the problem of "gluing" perverse sheaves. We also outline some of the most important applications to Representation theory and Topology of singular spaces. The contents of the lectures has effectively no overlapping with Borel's book " Algebraic Dmodules".

Authors: Ginzburg V.  Pages: 103 Year: 1998 
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