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Seminario Dottorato: “An introduction to Riemann-Hilbert correspondence”

Wednesday 8 May 2019, h.14:30 - Room 2BC30 - Davide Barco

ARGOMENTI: Seminars Ph.D. Program

Wednesday 8 May 2019, h.14:30, Room 2BC30
Davide Barco (Padova, Dip. Mat.)
“An introduction to Riemann-Hilbert correspondence”

Abstract
The 21st Hilbert problem concerns the existence of a certain class of linear differential equations on the complex affine line with specified singular points and monodromic groups. Arising both as an answer and an extension to this issue, Riemann-Hilbert correspondence aims to establish a relation between systems of linear differential equations defined on a complex manifold and suitable algebraic objects encoding topological properties of the same systems. The goal was first achieved for systems with regular singularities, thanks to the works by Deligne, Kashiwara and Mebkhout. Moreover, Deligne and Malgrange established a generalized correspondence (called Riemann-Hilbert-Birkhoff correspondence) for systems with irregular singularities on complex curves, encoding and describing the Stokes phenomenon which arises in this case. In more recent years, the correspondence has been extended to take account of irregular points on complex manifolds of any dimension by D'Agnolo and Kashiwara. In this talk we give a basic introduction on the subject by providing concepts and classical example from the theory.

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