Speaker: Dr. Finn Wiersig (National University of Singapore)

Title: A Riemann-Hilbert correspondence for D-cap-ModulesⅠ &Ⅱ & Ⅲ & Ⅳ

Venue & Time: MCM110

9:30-11:00  May 20, 2026 (Wednesday) &

13:00-14:30  May 22, 2026 (Friday) &

9:30-11:00  May 25, 2026 (Monday) &

9:30-11:00  May 27, 2026 (Wednesday)

Abstract: I discuss work on a Riemann-Hilbert correspondence for modules over Ardakov-Wadsley's sheaf D-cap of infinite order differential operators on a smooth rigid-analytic variety.

I will give four lectures. The first lecture provides an overview of the foundational theory of D-cap modules, as developed by Ardakov-Wadsley. In the second lecture, we introduce and motivate a solution functor for D-cap modules. We construct it using a decompletion of Fontaine's BdR, which we call the overconvergent de Rham period ring. In the third lecture, we prove that the solution functor is fully faithful. A key ingredient of our proof is the computation of the Galois cohomology of the overconvergent de Rham period ring. The final lecture, based on joint work in progress with Konstantin Ardakov, explores explicit computations of the solution functor. These examples suggest a conjecture: the solutions of many D-cap-modules are constructible, drawing a parallel with Kashiwara's classical constructibility theorem.