An Introduction to Riemann-Hilbert Correspondence for (algebraic) Regular Holonomic D-modules
Abstract:
D-module now plays a significant role in algebraic geometry, representation theory and arithmetic geometry. Nevertheless, the original idea of inventing D-modules is to find the solution spaces for systems of linear partial differential equations.
One of the most successful achievements of carrying forward this original idea is the Riemann-Hilbert correspondence: an equivalence of categories between the bounded derived category of (algebraic) regular holonomic D-modules and bounded derived category of (algebraically) constructible sheaves.
The goal of this talk is to explain why such correspondence is essentially solving systems of linear ordinary differential equations with regular singularities.
