Classical Analysis

Seminar information archive ~02/25Next seminarFuture seminars 02/26~


2023/10/31

10:30-14:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Benedetta Facciotti (University of Birmingham) 10:30-11:30
The Wild Riemann-Hilbert Correspondence via Groupoid Representations (ENGLISH)
[ Abstract ]
In this talk, through simple examples, I will explain the basic idea behind the Riemann-Hilbert correspondence. It is a correspondence between two different moduli spaces: the de Rham moduli space parametrizing meromorphic differential equations, and the Betti moduli space describing local systems of solutions and the representations of the fundamental group defined by them. We will see why such a correspondence breaks down for higher order poles.
Nikita Nikolaev (University of Birmingham) 13:30-14:30
The Wild Riemann-Hilbert Correspondence via Groupoid Representations (ENGLISH)
[ Abstract ]
I will explain an approach to extending the Riemann-Hilbert correspondence to the setting of equations with higher-order poles using the representation theory of holomorphic Lie groupoids. Each Riemann-Hilbert problem is associated with a suitable Lie algebroid that is integrable to a holomorphic Lie groupoid that can be explicitly constructed as a blowup of the fundamental groupoid. Then the Riemann-Hilbert correspondence can be formulated in rather familiar Lie theoretic terms as the correspondence between representations of algebroids and groupoids. An advantage of this approach is that groupoid representations can be investigated geometrically. Based on joint work with Benedetta Facciotti (Birmingham) and Marta Mazzocco (Birmingham), as well as joint work with Francis Bischoff (Regina) and Marco Gualtieri (Toronto).