2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Collection 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Organizer(s) Canary, Richard ; Garcia-Faide, Elba ; Labourie, François ; Li, Qiongling ; Neitzke, Andrew ; Pozzetti, Beatrice ; Wienhard, Anna

Date(s) 19/05/2025 - 27/05/2025

linked URL https://indico.math.cnrs.fr/event/11569/

22 23

Isomonodromic deformations, exact WKB analysis and Painlevé 1

By Olivier Marchal

In this talk, I will present how to obtain explicit formulas for the Hamiltonians and Lax matrices arising in isomonodromic deformations of generic rank 2 connections. Then, I will present how to proceed in the reverse way, i.e. how to build formal wave matrices solutions to a Lax system from a classical spectral curve using Topological Recursion. Finally I will discuss on the Painlevé 1 example, how one can upgrade formal power solutions to analytic solution known as tritronquées solutions of Painlevé 1 and how to define exact WKB on the formal wave matrix to formulate a corresponding Riemann-Hilbert problem via the characterization of the Stokes matrices.

Information about the video

Date of recording 27/05/2025
Date of publication 27/05/2025
Institution IHP
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Alexandre Duplessis
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2025.T2.WS1.022
Cite this video Marchal, Olivier (27/05/2025). Isomonodromic deformations, exact WKB analysis and Painlevé 1. IHP. Audiovisual resource. DOI: 10.57987/IHP.2025.T2.WS1.022
URL https://dx.doi.org/10.57987/IHP.2025.T2.WS1.022

Domain(s)

Mathematical Physics

MSC codes

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