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Quantisation of moduli spaces: Hitchin connections and isomonodromic deformations (QuantMod)
Marie Skłodowska-Curie Postdoctoral Fellowship (Global Fellowship), grant agreement 101108575
Université de Montpellier (IMAG) and University of Maryland (2023–2026)
Supervisors: D. Calaque (Montpellier) and R. A. Wentworth (Maryland)
EU project page: CORDIS
This page keeps track of the research output of QuantMod: it will be updated as the papers are published, and as further projects started during the fellowship come to completion.
The project (in brief, for non-experts)
Many phenomena in physics and geometry are governed by differential equations whose solutions can be deformed continuously while keeping certain essential features (their "monodromy") unchanged.
These are isomonodromic deformations, and they include the famous Painlevé equations.
QuantMod studies the space of deformation parameters, as well as the quantum counterparts of these deformations: in particular, it constructs families of quantum spaces that vary consistently with parameters, and it describes the symmetries ("wild mapping class groups") that act on them when the parameters are moved along loops.
Research output
All results are openly available on the arXiv, cf. Research.
- Papers originating during the fellowship:
-- Wild orbits and generalised singularity modules: stratifications and quantisation, with D. Calaque, G. Felder and R. A. Wentworth, arXiv:2402.03278. Accepted in Memoirs of the European Mathematical Society.
-- Moduli spaces of untwisted wild Riemann surfaces, with J. Douçot and M. Tamiozzo, arXiv:2403.18505. Conditionally accepted in Moduli, subject to minor revisions requested by the referee.
-- Twisted local G-wild mapping class groups, with J. Douçot and D. Yamakawa, arXiv:2504.01701. New extended version forthcoming.
-- Wild genus-zero quantum de Rham spaces, with M. Chaffe and D. Yamakawa, arXiv:2510.17666. Submitted.
- Earlier preprints revised and published during the fellowship:
-- Local wild mapping class groups and cabled braids, with J. Douçot and M. Tamiozzo, arXiv:2204.08188. Annales de l'Institut Fourier (online first, 2026).
-- Twisted local wild mapping class groups: configuration spaces, fission trees and complex braids, with P. Boalch and J. Douçot, arXiv:2209.12695. Publ. RIMS 61 (2025).
-- Sp(1)-symmetric hyperkähler quantisation, with J. E. Andersen and A. Malusà, arXiv:2111.03584. Pacific J. Math. 329 (2024).
Acknowledgements
This project has received funding from the European Union's Horizon Europe research and innovation programme, under the Marie Skłodowska-Curie grant agreement No 101108575.
Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Executive Agency (REA).
Neither the European Union nor the granting authority can be held responsible for them.
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