Eugen Bronasco

Postdoctoral researcher at Chalmers and GU

Chalmers webpage

Geometric Numerical Integration, Backward Error Analysis, Butcher Series, Combinatorial Hopf Algebras, Stochastic Differential Equations, Langevin Dynamics

bronasco [at] chalmers.se

About me

I am a postdoctoral researcher (since 2025) at Chalmers University of Technology and the University of Gothenburg, working in the group of Klas Modin. My research focuses on the geometric properties of time discretizations of the Euler–Zeitlin equation, which arises as a space discretization of the vorticity formulation of the incompressible Euler equation on the 2D sphere.

I was a Ph.D. student (2021–2025) at the University of Geneva under the supervision of Dominique Manchon and Gilles Vilmart. I received Prix Henri Fehr 2025 for the best doctoral thesis in mathematics of the year at the University of Geneva.

My research interests lie in numerical analysis, geometric numerical integration, and the algebraic structures underlying numerical methods for differential equations. I am particularly interested in developing new mathematical tools for the analysis and construction of numerical integrators, with an emphasis on methods that preserve geometric, algebraic, or statistical structures of the underlying differential equations.

My work combines techniques from numerical analysis, differential geometry, and combinatorial algebra. I study structures such as Butcher series, pre-Lie and Hopf algebras, and their extensions to settings involving geometric and stochastic differential equations. More broadly, I am interested in how these structures can be used to understand backward error analysis, structure-preserving discretizations, and the long-time behavior of numerical methods.

Publications

  1. E. B., Mechthild Thalhammer, (2026)
    Convergence analysis of generalized modified splitting methods using multi-index series,
    arXiv:2608.16356.
    https://doi.org/10.48550/arXiv.2608.16356
  2. E. B., Klas Modin, (2026)
    Backward error analysis for matrix discretizations of 2-D Euler equations,
    arXiv:2607.09549.
    https://doi.org/10.48550/arXiv.2607.09549
  3. E. B., Jean-Luc Falcone, Gilles Vilmart, (2026)
    Arboretum.hs: Symbolic manipulation for algebras of graphs,
    arXiv:2604.25879.
    https://doi.org/10.48550/arXiv.2604.25879
  4. E. B., Joscha Fregin, Daniel Ruprecht, Gilles Vilmart, (2026)
    Spectral Deferred Corrections in the framework of Runge-Kutta methods,
    arXiv.2604.03013.
    https://doi.org/10.48550/arXiv.2604.03013
  5. E. B., (2025)
    Algebraic structures and numerical methods for invariant measure sampling of Langevin dynamics,
    10.13097/archive-ouverte/unige:185162.
    https://doi.org/10.13097/archive-ouverte/unige:185162
  6. E. B., Adrien Busnot Laurent, Baptiste Huguet, (2025)
    High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods,
    arXiv.2503.21855.
    https://doi.org/10.48550/arXiv.2503.21855
  7. E. B., Benedict Leimkuhler, Dominic Phillips, Gilles Vilmart, (2025)
    Efficient Langevin sampling with position-dependent diffusion,
    arXiv:2501.02943.
    https://doi.org/10.48550/arXiv.2501.02943
  8. E. B., Adrien Busnot Laurent, (2026)
    Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations,
    Numerische Mathematik.
    https://doi.org/10.1007/s00211-026-01533-7
  9. E. B., (2024)
    Exotic B-series and S-series: algebraic structures and order conditions for invariant measure sampling,
    Foundations of Computational Mathematics.
    https://doi.org/10.1007/s10208-023-09638-3

Software

  1. Planarforest, fork of planarforest,
    Draw planar, exotic, aromatic, stolonic, decorated, edge-decorated, colored forests in LaTeX using TikZ and PythonTeX.
  2. Arboretum: symbolic package for automatic computation,
    in collaboration with Jean-Luc Falcone and Gilles Vilmart.
    A framework for implementing algebras of trees, forests, and more general graphs.
  3. Generalized Modified Splitting Methods,
    A Python implementation of generalized modified splitting methods providing convergence order verification and high-order integrator construction using multi-index formalism. A MATLAB script confirming the convergence order of a sample method written by Mechthild Thalhammer is included.

Conferences and Seminars

  1. Foundations of Computational Mathematics (FoCM) 2026,
    July 8th -- 18th 2026, Vienna, Austria.
  2. SciCADE 2026,
    June 29th -- July 3th 2026, Edinburgh, UK.
  3. CANUM 2026,
    June 1st -- 5th 2026, Saint-Jacut-de-la-Mer, France.
  4. ENUMATH 2025,
    September 1st -- 5th 2025, Heidelberg, Germany.
  5. CAM Seminar,
    January 27th 2025, Gothenburg, Sweden.
  6. Workshop on Numerical methods for complex high-dimensional systems,
    July 23 -- 26th 2024, Jervis Bay NSW, Australia.
  7. SciCADE24,
    July 15 -- 19th 2024, Singapore.
  8. SciCADE24 Summer School,
    July 8 -- 12th 2024, Singapore.
  9. NUMRAD24 Summer School,
    June 11 -- 14th 2024, Lausanne, Switzerland.
  10. Constrained Dynamics, Stochastic Numerical Methods and the Modeling of Complex Systems,
    May 26 -- 31st 2024, Oberwolfach, Germany.
  11. Séminaire GAAO,
    June 13th 2023, Clermont-Ferrand, France.
  12. Swiss Numerics Day 2023,
    June 7th 2023, Bern, Switzerland.
  13. Algebraic and Combinatorial Perspectives in the Mathematical Sciences (ACPMS),
    December 9th 2022, online.
  14. Differential Equations and Numerical Analysis Seminar,
    September 14th 2022, Trondheim, Norway.
  15. Workshop in Geometry and Geometric integration (Geo2Int),
    September 7 -- 9th 2022, Bergen, Norway.
  16. International Conference on Scientific Computation and Differential Equations (SciCADE 2022),
    July 25 -- 29th 2022, Reykjavı́k, Iceland.
  17. 45eme Congrès National d'Analyse Numérique (CANUM 2020+2),
    June 13 -- 17th 2022, Évian-les-Bains, France.

Posters

  1. Using exotic aromatic forests to construct order two scheme for the invariant measure sampling of Langevin dynamics with variable diffusion,
    NUMRAD24 Summer School, June 11 -- 14th 2024, Lausanne, Switzerland.
  2. Exotic B-series and S-series: algebraic structures and order conditions for invariant measure sampling,
    SWICCOMAS Poster Competition, February 10th 2023, Lausanne, Switzerland.

Teaching Assistance

  1. Practical sessions of Numerical analysis (UNIGE, 2021 -- 2024).
  2. Mathematical programming laboratory (UNIGE, 2022).
  3. Geometric and stiff numerical methods for differential equations (UNIGE, 2022).