EVENT DETAILS AND ABSTRACT

Title: On the Riemann-Hilbert correspondence
Speaker: Andrea D’Agnolo
Speaker Info: University of Padova
Brief Description:
Special Note:
Abstract:

Hilbert’s twenty-first problem (also known as the Riemann-Hilbert problem) asks for the existence of linear ordinary differential equations with prescribed regular singularities and monodromy. In higher dimensions, Deligne formulated it as a correspondence between regular meromorphic flat connections and local systems. In the early eighties, Kashiwara generalized it to a correspondence between regular holonomic D-modules and perverse sheaves on a complex manifold. The analogous problem for possibly irregular holonomic D-modules has been standing for a long time. One of the difficulties was to find a substitute target to the category of perverse sheaves. In the 80’s, Deligne and Malgrange proposed a correspondence between meromorphic connections and Stokes filtered local systems which holds in the one dimensional case. A few years ago, in a joint work with Kashiwara we solved the problem for general holonomic D-modules in any dimension. The construction of the target category is based on the theory of ind-sheaves by Kashiwara-Schapira and uses Tamarkin’s work on symplectic topology. Among the main ingredients of the proof is the description of the structure of flat meromorphic connections due to Mochizuki and Kedlaya. I will illustrate the above, and provide examples in the one dimensional case using the Fourier-Laplace transform.