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Math Grad Seminars - Berkan Uze - Introduction to the Riemann-Hilbert Correspondence
Monday, 18. November 2019, 14:00 - 15:00

Introduction to the Riemann-Hilbert Correspondence

Berkan Uze


Abstract: This lecture is an introduction to the Riemann-Hilbert correspondence in its various incarnations. We will begin with a brief sketch of the classical Riemann-Hilbert problem, going back to Hilbert’s problem concerning monodromy representations of ODE with Fuchsian singularities. The main goal of the lecture is to introduce Deligne’s Riemann-Hilbert correspondence.

To this end we will present the equivalence between local systems and vector bundles with a flat connection on a complex manifold. We will sketch a proof of this equivalence in the case of flat connections with so-called regular singularities, and discuss why irregular singularities cannot be situated in the same framework. More ambitiously, following Deligne and Katz, we hope to frame the R-H correspondence as a GAGA-like "algebraization" problem. Time permitting, we will make some introductory remarks on Kashiwara and Mebkhout’s generalized Riemann-Hilbert correspondence. 


Date: Monday, November 18, 2019

Time: 14:00 

Place: TB130