##  [Riemann-Hilbert Correspondence](/riemann-hilbert-correspondence) 

  ##  [Riemann-Hilbert Correspondence](https://mathlogic.quantumdictionary.io/riemann-hilbert-correspondence-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.

 

 

 

 

 





 

 



 ##  [Riemann-Hilbert Correspondence](https://algebra.quantumdictionary.io/riemann-hilbert-correspondence-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

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.