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I am a postdoctoral researcher at the Scuola Internazionale Superiore di Studi Avanzati (Trieste) in the group of Prof. Ilya Chevyrev.
From 11/2022 to 12/2025 I was a postdoctoral researcher at the Max Planck Institute for Mathematics in the Sciences (Leipzig), in the group of Prof. Felix Otto.
From 09/2019 to 11/2022, I was a PhD student at the Laboratoire de Probabilités, Statistique et Modélisation (Paris) under the supervision of Prof. Lorenzo Zambotti and Prof. Cyril Labbé. You can find my PhD thesis here.
My mathematical interests are in the area of rough analysis. I am particularly interested in the theories of rough paths and regularity structures and in their applications to stochastic PDEs.
Mini-course in Edinburgh (25-26/02/2026): preliminary lecture notes are available here.
Publications and Preprints:
Renormalised Models for Variable Coefficient Singular SPDEs. Arxiv preprint (2025). (Joint with Rhys Steele and Harprit Singh)
Multi-index Based Solution Theory to the Φ4 Equation in the Full Subcritical Regime. Arxiv preprint (2025). (Joint with Felix Otto and Rhys Steele)
Lecture notes on Malliavin calculus in regularity structures. Stochastics and Partial Differential Equations: Analysis and Computations (2025). (Joint with Felix Otto and Markus Tempelmayr).
Hairer's multilevel Schauder estimates without Regularity Structures. Transactions of the American Mathematical Society 377 (2024), 6981-7035. (Joint with Francesco Caravenna and Lorenzo Zambotti).
The Sewing lemma for 0 < γ ≤ 1. Journal of Functional Analysis 283 (2022), no. 10, Paper No. 109644, 34 pp. (Joint with Lorenzo Zambotti).
Besov Reconstruction. Potential Analysis 59, 1875–1912 (2023). (Joint with David Lee).
An example of singular elliptic stochastic PDE. Matemática Contemporânea, Volume 58 – XXV Brazilian School of Probability (2023). (Joint with Francesco Caravenna and Lorenzo Zambotti).
Contributions to proceedings:
Integrability of $\Phi_2^4$. Oberwolfach Report 59 (2023), 3340-3343. (Joint with Wenhao Zhao).
Poster_PDE2026.pdfSummer School in Leipzig
Summer School in Leipzig
Together with Şefika Kuzgun, Peter Morfe, Felix Otto, Rhys Steele and Christian Wagner we are organising a 2nd Summer School on PDEs and Randomness at the Max Planck Institute for Mathematics in the Sciences in the week of the 13-17 July 2026.
Registration deadline: 28 February 2026.
My CV:
CV-Lucas-BROUX_lite.pdfPage updated
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