Speaker: Nikita Nikolaev

Title: The Wild Riemann-Hilbert Correspondence via Groupoid Representations Part 2

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).

This seminar is a part of the first TSVP Thematic Program "Exact Asymptotics: From Fluid Dynamics to Quantum Geometry" (https://groups.oist.jp/tsvp/exact-asymptotics). OIST students and researchers are welcome to participate in all scientific sessions of the program without registration.

List and profiles of program participants can be found here: https://groups.oist.jp/tsvp/23ea-program-participants