Appears in collection : Masaki Kashiwara and Pierre Schapira - Indsheaves, temperate holomorphic functions and irregular Riemann-Hilbert correspondence

The aim of the course is to describe the Riemann-Hilbert correspondence for holonomic D-modules in the irregular case and its applications to integral transforms with irregular kernels, especially the Laplace transform. The course will start with a detailed exposition of the theory of indsheaves (including sheaves on the subanalytic site) and its applications to the indsheaf of holomorphic temperate functions.