Abstract

The Riemann-Hilbert correspondence establishes a profound connection between certain differential equations on a given complex analytic manifold and its topology. This result had numerous interesting applications; for example, it was applied by Beilinson-Bernstein and Brylinski-Kashiwara in the 1980s to study the representation theory of semisimple algebraic groups. This talk explores ongoing research leveraging these concepts to investigate representation theory appearing in the p-adic local Langlands program, focusing on progress towards a p-adic analytic Riemann-Hilbert correspondence.