Decomposition theorem for semisimple algebraic holonomic D-modules

Decomposition theorem for perverse sheaves on algebraic varieties, proved by Beilinson-Bernstein-Deligne-Gabber, is one of the most important and useful theorems in the contemporary mathematics. By the Riemann-Hilbert correspondence, we may regard it as a theorem for regular holonomic D-modules of geometric origin. Rather recently, it was generalized to the context of semisimple holonomic D-modules which are not necessarily regular.

In this talk, we shall give an overview of the progress in the theory of holonomic D-modules motivated by the generalization of the decomposition theorem.