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:

• 2022-: Jacob Armstrong-Goodall, PhD Thesis, Principal supervisor, University of Edinburgh.

• 2020-: Usama Nadeem, PhD Thesis, Principal supervisor, University of Edinburgh.

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

• 2020-2022: Xingyuan Chen, PhD Thesis, Second supervisor, University of Edinburgh.

• 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, K. Ebrahimi-Fard, "Bogoliubov type recursions for renormalisation in regularity structures",
  to appear in Annales de l’Institut Henri Poincaré (D) Combinatorics, Physics and their Interactions (Accepted 12/09/2023), 29 pages, arxiv:2006.05284 .

• Y. Bruned, "Regularity Structures",
  16 pages, submitted to Encyclopedia of Mathematical Physics, Second edition, Elsevier. pdf .

• Y. Bruned, F. Katsetsiadis, "Post-Lie algebras in Regularity Structures",
  to appear in Forum Mathematics, Sigma (Accepted 04/08/2023), 25 pages, arxiv:2208.00514 .

• Y. Alama Bronsard, Y. Bruned, K. Schratz, "Approximation of dispersive PDEs in the presence of low-regularity randomness",
  to appear in Foundations of Computational Mathematics (Accepted 12/07/2023), 49 pages,
  arxiv:2205.02156 .

• Y. Bruned, P. Linares, "A top-down approach to algebraic renormalization in regularity structures based on multi-indices",
  65 pages, submitted, arxiv:2307.03036 .

• Y. Alama Bronsard, Y. Bruned, G. Maierhofer, K. Schratz, "Symmetric resonance based integrators and forest formulae",
  71 pages, submitted, arxiv:2305.16737 .

• 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 .

• I. Bailleul, Y. Bruned, "Parametrization of renormalized models for singular stochastic PDEs",
  to appear in Kyoto Journal of Mathematics (Accepted 24/01/2023), 17 pages,
  arxiv:2106.08932 .

• 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, 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, U. Nadeem, "Diagram-free approach for convergence of tree-based models in Regularity Structure",
  33 pages, submitted, arxiv:2211.11428.

• Y. Bruned, U. Nadeem, "Convergence of space-discretised gKPZ via Regularity Structures",
  58 pages, submitted, arxiv:2207.09946 .

• 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 .

• N. Berglund, Y. Bruned, "BPHZ renormalisation and vanishing subcriticality limit of the fractional \phi_d^3",
  52 pages, submitted, arxiv:1907.13028 .

• 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 .