Riemann-Hilbert Correspondence

A correspondence linking regular holonomic systems of linear differential equations (or regular holonomic D-modules, i.e. linear connections with regular singularities) on complex manifolds with representations of the fundamental group (local systems), pairing analytic solution data with topological monodromy data.

An equivalence (or correspondence) between categories of regular holonomic D-modules (or meromorphic connections with regular singularities) on a complex analytic manifold and categories of constructible sheaves or local systems (representations of the fundamental group) on the underlying topological space; it matches algebraic differential equations with their analytic monodromy data.