The Riemann-Hilbert Correspondence in Nonarchimedean Geometry

Let X be a smooth projective variety over the field of complex numbers. The classical Riemann-Hilbert correspondence supplies a fully faithful embedding from the category of perverse sheaves on X to the category of algebraic D_X-modules. In this talk, I'll describe joint work with Bhargav Bhatt on an analogous construction in the setting of non-archimedean geometry.