Irregular Riemann-Hilbert Correspondence: introduction to the problem

One of the most successful bridges between analysis and algebraic geometry is the classical Riemann-Hilbert (R-H) correspondence between regular holonomic D-modules and perverse sheaves on complex manifolds, where D is the sheaf of differential operators with holomorphic coefficients (proved independently by Kashiwara and Mebkhout in 1984). This correspondence is a far-reaching generalization of Hilbert’s 21st Problem asking about the existence