Title: Logarithmic Riemann-Hilbert Correspondences
Abstract: The classical Riemann-Hilbert Correspondence provides a deep connection between geometry and topology. In its simplest form it stipulates an equivalence between the categories of vector bundles with a flat connection on a complex manifold and local systems on the topological space underlying the manifold. If one allows the connection to have poles, the situation becomes considerably more subtle. We discuss work of Kato-Nakayama and Ogus on this "logarithmic" setting. This in turn motivates recent joint work with Mattia Talpo on a further generalization to logarithmic D-modules. We discuss how this conjectural log Riemann-Hilbert Correspondence should look and the progress that has been achieved so far.