Jean Douçot




Institut de Recherche Mathématique Avancée
7 rue René Descartes
67084 Strasbourg Cedex
France

Email: firstname.lastname[at]gmail.com or firstname.lastname[at]math.unistra.fr
Photo


I am a mathematician, currently employed as a postdoctoral researcher at IRMA in Strasbourg, as part of the DAG-Arts ANR project.

Before that, I did my Phd at the Paris-Saclay university, under the direction of Philip Boalch, then held several postdoctoral positions: at the University of Geneva, in the team of Anton Alekseev, then as a junior FCT researcher in the Group of mathematical physics in Lisbon, and at the Simion Stoilow Institute of Mathematics of the Romanian Academy in Bucharest as a member of the project Cohomological Hall algebras of smooth surfaces and applications led by Olivier Schiffmann.

You can find my CV here.

Research interests

My research deals with moduli spaces of meromorphic connections with irregular singularities on Riemann surfaces, which can also be viewed, via the Riemann-Hilbert-Birkhoff correspondence, as moduli spaces for their generalized monodromy data, a.k.a Stokes data, giving rise to wild character varieties.

I am also interested in the integrable systems which naturally arise from such moduli spaces, focussing on irregular isomonodromic deformations and their topological version, consisting of wild mapping class group actions on wild character varieties.

More specifically, a large part of my work is motivated by the question of the classification of these moduli spaces in genus zero, including the construction of combinatorial invariants for them, and the construction of explicit isomorphisms between different wild character varieties. I have also been interested in the explicit description of wild mapping class groups.

Some keywords: Meromorphic connections, irregular singularities, Stokes data, wild character varieties, isomonodromic deformations, Painlevé equations, Lax representations, wild mapping class groups, nonabelian Hodge theory, Fourier transform, nonabelian Hodge diagrams, fission trees.

Articles

  1. Combinatorics of the Fourier transform: Stokes data, Gale duality and frieze patterns, with Andreas Hohl, preprint, 2026.
  2. Fourier transform of irregular connections on P1 and classification of Argyres-Douglas theories, preprint, 2026.
  3. New nonabelian Hodge graphs from twisted irregular connections, preprint, 2025.
  4. Twisted local G-wild mapping class groups, with Gabriele Rembado and Daisuke Yamakawa, preprint, 2025.
  5. Simplification of exponential factors of irregular connections on P1, Bulletin of the London Mathematical Society, 2026.
  6. Basic representations of genus zero nonabelian Hodge spaces, SIGMA, 2026.
  7. Moduli spaces of untwisted wild Riemann surfaces, with Gabriele Rembado and Matteo Tamiozzo, preprint, 2024.
  8. A topological algorithm for the Fourier transform of Stokes data at infinity, with Andreas Hohl, Journal of the London Mathematical Society, 2025.
  9. Twisted local wild mapping class groups: configuration spaces, fission trees and complex braids, with Philip Boalch and Gabriele Rembado, PRIMS, 2025.
  10. Topology of irregular isomonodromy times on a fixed pointed curve, with Gabriele Rembado, Transformation groups, 2023.
  11. Local wild mapping class groups and cabled braids, with Gabriele Rembado and Matteo Tamiozzo, Annales de l'Institut Fourier, online first, 2026
  12. Diagrams and irregular connections on the Riemann sphere, preprint, 2021.

Some talks

Other scientific texts