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The Riemann-Hilbert correspondence yields an equivalence between the triangulated category of (regular holonomic) D-modules and that of constructible sheaves. Under this equivalence the abelian category of D-modules corresponds to the abelian category of perverse sheaves. In some contexts this abelian category has a concrete combinatorial description; in particular Kapranov and Schechtman showed that this is the case for perverse sheaves on real hyperplane arrangements. Such perverse sheaves arise from (some) GKZ systems of differential equations. We will look at those perverse sheaves, and describe their categorification, i.e. perverse schobers. This is joint work with Michel Van den Bergh.