Personal Webpage of Adrien BUSNOT LAURENT

Publications:

• Adrien Busnot Laurent, Hans Munthe-Kaas, Venkatesh G. S., The free tracial post-Lie-Rinehart algebra of planar aromatic trees for the design of divergence-free Lie-group methods.
  
  
  
• Adrien Busnot Laurent, Kristian Debrabant, Anne Kværnø, Derivation of optimal stochastic Runge-Kutta methods with exotic and decorated Butcher series for the weak integration of stochastic dynamics.
  
  
  
• Zhicheng Zhu, Adrien Busnot Laurent, Aromatic and clumped multi-indices: algebraic structure and Hopf embeddings.
  
  
  
• Adrien Busnot Laurent, Yunnan Li, Yunhe Sheng, Post-Hopf algebroids, post-Lie-Rinehart algebras and geometric numerical integration.
  
  
  
• Charles-Edouard Bréhier, Adrien Busnot Laurent, Arnaud Debussche, Gilles Vilmart, Preconditioning for the high-order sampling of the invariant distribution of parabolic semilinear SPDEs.
  
  
  
• Eugen Bronasco, Adrien Busnot Laurent, Baptiste Huguet, High order integration of stochastic dynamics on Riemannian manifolds with frozen flow methods.
  
  
  
• Adrien Busnot Laurent, Oscar Cosserat, Butcher series for Hamiltonian Poisson integrators through symplectic groupoids.
  
  
  
• Karine Beauchard, Adrien Laurent, Frédéric Marbach, Control theory and splitting methods.
  
  
  
• Eugen Bronasco, Adrien Laurent, Hopf algebra structures for the backward error analysis of ergodic stochastic differential equations, Numer. Math., pages 1–61 (2026).
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• Adrien Laurent, The Lie derivative and Noether's theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators, Journal of Computational Dynamics, Special issue on mechanics, computation and their math foundations, 2024, 11(1): 10-22.
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• Adrien Laurent, Hans Z. Munthe-Kaas, The universal equivariance properties of exotic aromatic B-series, Found. Comput. Math. (2025), 25(5):1595-1626.
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• Adrien Laurent, Robert I. McLachlan, Hans Z. Munthe-Kaas, Olivier Verdier, The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators, Forum of Mathematics Sigma 11 (2023), E69.
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• Adrien Laurent, A uniformly accurate scheme for the numerical integration of penalized Langevin dynamics, SIAM J. Sci. Comput. 44 (2022), no. 5, A3217-A3243.
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• Adrien Laurent, Gilles Vilmart, Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds, Found. Comput. Math. 22 (2022), 649–695.
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• Adrien Laurent, Gilles Vilmart, Multirevolution integrators for differential equations with fast stochastic oscillations, SIAM J. Sci. Comput. 42 (2020), no. 1, A115–A139.
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• Adrien Laurent, Gilles Vilmart, Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs, Math. Comp. 89 (2020), 169-202.
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Conference reports and proceedings:

• Adrien Laurent, High order integration of stochastic dynamics in R^d, on manifolds, and in the neighbourhood of manifolds, Oberwolfach Report No. 26/2024.
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Thesis:

• Algebraic Tools and Multiscale Methods for the Numerical Integration of Stochastic Evolutionary Problems, Ph.D. Thesis, University of Geneva (2021), No. 5570.
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Software:

• The Python package HomotoPy for manipulating the aromatic forms and the aromatic bicomplex. HomotoPy represents aromatic forests as dictionaries. It contains the functions from the papers (Euler operators, horizontal, vertical, variational derivatives, homotopy operators, Lie derivative...), as well as understandable examples to manipulate the bicomplex.
  Here is the article describing the aromatic bicomplex (see also the article on the Lie derivative).
• Uniformly accurate integrator for the weak approximation of overdamped Langevin dynamics in the neighbourhood of a manifold (in Julia).
  Here is the associated Yareta archive and article.
• High order integrators for sampling the invariant measure of constrained overdamped Langevin dynamic (in Julia).
  Here is the associated Yareta archive and article.
• Multirevolution integrators for SDEs with fast stochastic oscillations and the nonlinear Schrödinger equation with fast white noise dispersion (in Julia).
  Here is the associated Yareta archive and article.

Posters:

• Order conditions for sampling the invariant measure of ergodic SDEs in R^d or on manifolds, Workshop on Multiscale Methods for Deterministic and Stochastic Dynamics, 2020.
• Exotic aromatic B-series for the study of long time integrators for a class of ergodic SDEs, SciCADE, 2017.