Research Interests:
- Singular Stochastic Partial Differential Equations (SPDEs).
- Generalised KPZ equation.
- Renormalisation and Hopf Algebra.
- Dispersive Partial Differential Equations.
Supervision of postdoctoral researchers:
- 10/2024-: Paul Laubie, Postdoctoral researcher, Université de Lorraine.
- 2024-: Carlo Bellingeri, Postdoctoral researcher, Université de Lorraine.
Supervision fo PhD students:
- 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-: Jacob Armstrong-Goodall, PhD Thesis, 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: 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, L. Tolomeo, "Cancellations for dispersive PDEs with random initial data",
25 pages, submitted, arxiv:2412.17051.
- Y. Bruned, Y. Hou "Multi-indices coproducts from ODEs to singular SPDEs",
To appear in Transactions of the American Society (Accepted 21/12/2024), 31
pages. arxiv:2405.11314.
- 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.
- 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 .
- N. Berglund, Y. Bruned, "BPHZ renormalisation and vanishing subcriticality limit of the
fractional \phi_d^3",
Stochastics and Partial Differential Equations: Analysis and Computations,
2024, 65 pages.
arxiv:1907.13028 .
doi:10.1007/s40072-024-00331-2 .
- 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, K. Ebrahimi-Fard, "Bogoliubov type recursions for renormalisation in regularity
structures",
Annales de l’Institut Henri Poincaré (D) Combinatorics,
Physics and their Interactions, 2024, 31 pages.
arxiv:2006.05284 .
doi:10.4171/AIHPD/186 .
- 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, "Composition and substitution of Regularity Structures B-series",
31 pages, submitted, arxiv:2310.14242 .
- Y. Bruned, "Regularity Structures",
16 pages, submitted to Encyclopedia of Mathematical
Physics,
Second edition, Elsevier. pdf .
- Y. Alama Bronsard, Y. Bruned, G. Maierhofer, K. Schratz, "Symmetric resonance based
integrators and forest formulae",
71 pages, submitted, arxiv:2305.16737 .
- I. Bailleul, Y. Bruned, "Random models for singular SPDEs",
15 pages, submitted, arxiv:2301.09596 .
- Y. Bruned, F. Katsetsiadis, “Geometric embeding for Regularity Structures”,
26 pages, submitted, arxiv:2301.05896 .
- 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 .
- I. Bailleul, Y. Bruned, "Locality for singular stochastic PDEs",
14 pages, submitted, arxiv:2109.00399 .
- 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 .
- I. Bailleul, Y. Bruned, "Renormalised singular stochastic PDEs",
16 pages, submitted, arxiv:2101.11949 .
- 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, "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 .
- 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
.