Riemann-Hilbert on contact manifolds

We present a microlocal refinement of the Riemann–Hilbert correspondence, extending the classical equivalence between holomorphic vector bundles with connection and local systems. The talk will begin with background on constructible sheaves, D-modules, and their microlocalization, followed by an explanation of the classical correspondence and its microlocal analogues. We conclude with an application to WKB operators on exact symplectic manifolds, highlighting connections to geometric representation theory—specifically to the Category O of symplectic resolutions studied by Braden, Licata, Proudfoot, and Webster. This is joint work with Laurent Côté, David Nadler, and Vivek Shende.