Yvain BRUNED
Research

Research Interests:

• Singular Stochastic Partial Differential Equations (SPDEs).

• Generalised KPZ equation.

• Regularity Structures.

• Renormalisation and Hopf Algebra.

• Rough Paths.

• Numerical Analysis.

• Dispersive Partial Differential Equations.

Supervision of postdoctoral researchers:

• 09/2025-: Nicolas Moench, Postdoctoral researcher, Université de Lorraine.

• 10/2024-: Paul Laubie, Postdoctoral researcher, Université de Lorraine.

• 01/2024-08/2025: Carlo Bellingeri Postdoctoral researcher, Université de Lorraine.
  Maître de Conférences since 09/2025, Université de Haute-Alsace, Mulhouse.

Supervision of PhD students:

• 11/2025-: Valentin Clarisse, PhD Thesis, Principal supervisor, Université de Lorraine.

• 09/2025-: Hugo Nouaille, PhD Thesis, Principal supervisor, Université de Lorraine.

• 2024-: Aurélien Minguella, PhD Thesis, Principal supervisor, Université de Lorraine.

• 2023-: Yingtong Hou, PhD Thesis, Principal supervisor, Université de Lorraine.

• 2022-2025: Jacob Armstrong-Goodall, PhD Thesis (Viva 13/07/2025), Principal supervisor, University of Edinburgh.

• 2020-2024: Usama Nadeem, PhD Thesis (Viva 23/08/2024), Principal supervisor, University of Edinburgh.

• 2019-2023: Foivos Katsetsiadis, PhD Thesis (Viva 01/09/2023), Principal supervisor, University of Edinburgh.

Supervision of Master/Bachelor students

• 2024-2025: Valentin Clarisse, Stage de Master 2, Sorbonne Université.

• 2024-2025: Ismaël Wahoub, Parcours recherche, Mines de Nancy, Université de Lorraine.

• 2022-2023: Sophie Baland, Stage de Master 2, Université de Lorraine.

• 2021-2022: Hou Yingtong, Master Thesis, University of Edinburgh.

• 2021-2022: Wei Lun, Master Thesis, University of Edinburgh.

• 2020-2021: Rachel Dance, Master Thesis, University of Edinburgh.

• 2020-2021: Li Wenjie, Master Thesis, University of Edinburgh.

• 2020-2021: Zhang Hanwen, Master Thesis, University of Edinburgh.

• 2019-2020: Chen Kaili, Master Thesis, University of Edinburgh.

• 2019-2020: Qian Yiming, Master Thesis, University of Edinburgh.

• 2019-2020: Xie Qingyu, Master Thesis, University of Edinburgh.

• 2018-2019: Yu Yue, Master Thesis, University of Edinburgh.

• 2018-2019: Song Zihao, Master Thesis, University of Edinburgh.

• 2021-2022: Vegard Solberg, Bachelor Thesis, University of Edinburgh.

• 2021-2022: Ella YU, Bachelor Thesis, University of Edinburgh.

Publications:

• Y. Bruned, A. Minguella, “Recentering with Malliavin derivative”,
  18 pages, submitted, arxiv:2603.03261.

• I. Bailleul, Y. Bruned, "Locality for singular stochastic PDEs",
  Annals of Probability, March 2026, Volume 54, Issue 2, pp 768-795. arxiv:2109.00399 . doi:10.1214/25-AOP1778 .

• I. Bailleul, Y. Bruned, "Renormalised singular stochastic PDEs",
  16 pages, merged with "Locality for singular SPDEs", arxiv:2101.11949 .

• Y. Bruned, Y. Hou, P. Laubie, Z. Zhu, “Banach fixed point and flow approach for rough analysis”,
  29 pages, submitted, arxiv:2602.17437.

• I. Bailleul, Y. Bruned, "Random models for singular SPDEs",
  Stochastics and Partial Differential Equations: Analysis and Computations, 2026, 31 pages.
  arxiv:2301.09596 . doi:10.1007/s40072-026-00414-2 .

• Y. Bruned, “Derivation of resonance-based schemes via normal forms”,
  36 pages, submitted, arxiv:2511.07838.

• C. Bellingeri, Y. Bruned, Y. Hou, "Flows driven by multi-indices Rough Paths",
  Journal of Differential Equations, February 2026, Volume 453, Part 5, 113931.
  arxiv:2502.14771. doi:10.1016/j.jde.2025.113931 .

• Y. Bruned, P. Laubie, “Elementary differentials from multi-indices to rooted trees”,
  24 pages, submitted, arxiv:2509.13118.

• Y. Alama Bronsard, Y. Bruned, G. Maierhofer, K. Schratz, "Symmetric resonance based integrators and forest formulae",
  To appear in Foundations of Computational Mathematics (Accepted 15/09/2025), 76 pages. arxiv:2305.16737 .

• Y. Bruned, "Decorated Trees, Arborification for Cancellations in Wave Turbulence",
  Séminaire Laurent Schwartz, EDP et applications (2024-2025), Exposé no. 16, 15 pages.
  doi:10.5802/slsedp.180 .

• J. Armstrong-Goodall, Y. Bruned, “Birkhoff normal form via decorated trees”,
  22 pages, submitted, arxiv:2505.04547.

• Y. Bruned, Y. Sheng, R. Tang, “Post-Lie deformations of pre-Lie algebras and their applications in Regularity Structures”,
  16 pages, submitted, arxiv:2505.00456.

• Y. Bruned, F. Rousset, K. Schratz, “Resonances and computations”,
  25 pages, submitted, arxiv:2504.19647.

• Y. Bruned, A. Minguella, "Renormalisation in the flow approach for singular SPDEs",
  48 pages, submitted, arxiv:2504.04885.

• Y. Bruned, K. Ebrahimi-Fard, "Bogoliubov type recursions for renormalisation in regularity structures",
  Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions, 2025, Volume 12,
  Issue 4, pp 673-703. arxiv:2006.05284 . doi:10.4171/AIHPD/186 .

• N. Berglund, Y. Bruned, "BPHZ renormalisation and vanishing subcriticality limit of the fractional \phi_d^3",
  Stochastics and Partial Differential Equations: Analysis and Computations, Juin 2025, Volume 13, pp 243-307.
  arxiv:1907.13028 . doi:10.1007/s40072-024-00331-2 .

• Y. Bruned, Y. Hou "Multi-indices coproducts from ODEs to singular SPDEs",
  Transactions of the American Mathematical Society, pp 1-28. arxiv:2405.11314. doi:10.1090/tran/9411.

• Y. Bruned, F. Katsetsiadis, “Geometric embeding for Regularity Structures”,
  To appear at Annales de la Faculté des Sciences de Toulouse, (Accepted 25/03/2025), 27 pages.
  arxiv:2301.05896 .

• Y. Bruned, "Regularity Structures",
  Encyclopedia of Mathematical Physics, 2025, Volume 5, pp 16-23, Second edition, Elsevier.
  pdf . doi:10.1016/B978-0-323-95703-8.00073-2.

• Y. Bruned, K. Ebrahimi-Fard, Y. Hou, "Multi-indice B-series",
  Journal of the London Mathematical Society, 2025, Volume 111, Issue 1, e70049.
  arxiv:2402.13971. doi:10.1112/jlms.70049.

• Y. Bruned, Y. Hou, "Renormalising Feynman diagrams via multi-indices",
  40 pages, submitted, arxiv:2501.08151.

• Y. Bruned, L. Tolomeo, "Cancellations for dispersive PDEs with random initial data",
  25 pages, submitted, arxiv:2412.17051.

• Y. Bruned, P. Linares, "A top-down approach to algebraic renormalization in regularity structures based on multi-indices",
  Archive for Rational Mechanics and Analysis, 2024, Volume 248, Article 111, pp 1-81.
  arxiv:2307.03036 . doi:10.1007/s00205-024-02041-4.

• J. Armstrong-Goodall, Y. Bruned, "Low regularity symplectic schemes for stochastic NLS",
  30 pages, submitted, arxiv:2410.22359.

• I. Bailleul, Y. Bruned, "Parametrization of renormalized models for singular stochastic PDEs",
  Kyoto Journal of Mathematics November 2024, Volume 64, Issue 4, pp 829-854.
  arxiv:2106.08932 . doi:10.1215/21562261-2024-0006.

• Y. Bruned, U. Nadeem, "Diagram-free approach for convergence of tree-based models in Regularity Structure",
  Journal of the Mathematical Society of Japan, October 2024, Volume 76, Issue 4, pp 1139-1169.
  arxiv:2211.11428. doi:10.2969/jmsj/91129112 .

• C. Bellingeri, Y. Bruned, "Symmetries for the gKPZ equation via multi-indices",
  30 pages, submitted, arxiv:2410.00834 .

• Y. Bruned, "Derivation of normal forms for dispersive PDEs via arborification",
  29 pages, submitted, arxiv:2409.03642.

• Y. Alama Bronsard, Y. Bruned, K. Schratz, "Approximation of dispersive PDEs in the presence of low-regularity randomness",
  Foundations of Computational Mathematics, 2024, Volume 24, pp 1819-1869.
  arxiv:2205.02156 . doi:10.1007/s10208-023-09625-8 .

• Y. Bruned, U. Nadeem, "Convergence of space-discretised gKPZ via Regularity Structures",
  Annals of Applied Probability, 2024, Volume 34, Issue 2, pp 2488-2538. arxiv:2207.09946 . doi:10.1214/23-AAP2029 .

• Y. Bruned, V. Dotsenko "Chain rule symmetry for singular SPDEs",
  42 pages, submitted, arxiv:2403.17066 .

• Y. Bruned, M. Gerencsér, U. Nadeem, "Quasi-generalised KPZ equation",
  57 pages, submitted, arxiv:2401.13620 .

• J. Armstrong-Goodall, Y. Bruned, "Resonance based schemes for SPDEs",
  35 pages, submitted, arxiv:2312.16690 .

• Y. Bruned, V. Dotsenko, "Novikov algebras and multi-indices in regularity structures",
  23 pages, submitted, arxiv:2311.09091 .

• Y. Bruned, F. Katsetsiadis, "Post-Lie algebras in Regularity Structures",
  Forum Mathematics, Sigma, 2023, Volume 11, e98, pp 1-20.
  arxiv:2208.00514 . doi:10.1017/fms.2023.93 .

• Y. Bruned, "Composition and substitution of Regularity Structures B-series",
  31 pages, submitted, arxiv:2310.14242 .

• Y. Bruned, D. Manchon, "Algebraic deformation for (S)PDEs",
  Journal of the Mathematical Society of Japan, April 2023, Volume 75, Issue 2, pp 485-526.
  arxiv:2011.05907 . doi:10.2969/jmsj/88028802 .

• Y. Bruned, F. Katsetsiadis, "Ramification of Volterra-type Rough Paths",
  Electronic Journal of Probability, 2023, Volume 28, pp 1-25.
  arxiv:2105.03423 . doi:10.1214/22-EJP890 .

• Y. Bruned, "Renormalisation from non-geometric to geometric rough paths",
  Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 2022, Volume 58, Issue 2, pp 1078-1090.
  arxiv:2007.14385 . doi:10.1214/21-AIHP1178 .

• Y. Alama Bronsard, Y. Bruned, K. Schratz, "Low regularity integrators via decorated trees",
  57 pages, submitted, arxiv:2202.01171.

• Y. Bruned, K. Schratz, "Resonance based schemes for dispersive equations via decorated trees",
  Forum of Mathematics, Pi, 2022, Volume 10, e2, pp 1-76.
  arxiv:2005.01649 . doi:10.1017/fmp.2021.13 .

• Y. Bruned, F. Gabriel, M. Hairer, L. Zambotti, "Geometric stochastic heat equations",
  Journal of the American Mathematical Society, 2022, Volume 35, Issue 1, pp 1-80.
  arxiv:1902.02884 . doi:10.1090/jams/977 .

• Y. Bruned, A. Chandra, I. Chevyrev, M. Hairer, "Renormalising SPDEs in regularity structures",
  Journal of the European Mathematical Society, 2021, Volume 23, Issue 3, pp 869-947.
  arxiv:1711.10239 . doi:10.4171/JEMS/1025 .

• Y. Bruned, M. Hairer, L. Zambotti, "Renormalisation of Stochastic Partial Differential Equations",
  EMS Newsletter, March 2020, Volume 115, Issue 3, pp 7–11. doi:10.4171/NEWS/115/3 .

• Y. Bruned, C. Curry, K. Ebrahimi-Fard, "Quasi-shuffle algebras and renormalisation of rough differential equations",
  Bulletin of the London Mathematical Society, February 2020, Volume 52, Issue 1, pp 43-63.
  arxiv:1801.02964 , doi:10.1112/blms.12305 .

• Y. Bruned, I. Chevyrev, P. Friz, R. Preiss, "A rough path perspective on renormalization",
  Journal of Functional Analysis, December 2019, Volume 277, Issue 11, 108283.
  arxiv:1701.01152 , doi:10.1016/j.jfa.2019.108283 .

• Y. Bruned, M. Hairer, L. Zambotti, "Renormalisation algébrique des structures de régularité",
  8 pages, Letter of INSMI, June 2019. URL: https://www.insmi.cnrs.fr/sites/institut_insmi/files/news/2020-02/renormalisation_algebrique.pdf .

• Y. Bruned, M. Hairer, L. Zambotti, "Algebraic renormalisation of regularity structures",
  Inventiones Mathematicae, March 2019, Volume 215, Issue 3, pp 1039-1156,
  arxiv:1610.08468 , doi:10.1007/s00222-018-0841-x .
  This paper opens new perspectives in the renormalisation field. It was the central topic of a workshop at the University of Bergen from the 3rd to the 7th of April 2017, organised by Dominique Manchon, Hans Munthe-Kaas and Kurusch Ebrahimi-Fard.
  

• Y. Bruned, "Recursive formulae in regularity structures",
  Stochastics and Partial Differential Equations: Analysis and Computations, December 2018, Volume 6, Issue 4, pp 525-564, arxiv:1710.10634 , doi:10.1007/s40072-018-0115-z .

• Y. Bruned, I. Chevyrev, P. Friz, "Examples of renormalized SDEs",
  Stochastic Partial Differential Equations and Related Fields. Springer International Publishing, 2018, pp 303-317, arxiv:1701.01158 , doi:10.1007/978-3-319-74929-7_19 .

• Y. Bruned, "Singular KPZ type equations",
  205 pages, PhD thesis, Université Pierre et Marie Curie, 2015, URL: https://tel.archives-ouvertes.fr/tel-01306427 .

• M. Arzel, C. Lahuec, C. Jego, W. Gross, and Y. Bruned, "Stochastic multiple stream decoding of cortex codes", Signal Processing, IEEE Transactions on, vol. 59, no. 7, pp. 3486 –3491, july 2011. doi:10.1109/TSP.2011.2138699 .