I am a PhD student at CMAP (applied mathematics lab in École polytechnique), under the supervision of François Alouges and Aline Lefebvre-Lepot.

I study partial differential equations and numerical methods, and I also focus on optimizing numerical simulations, applied to swimming at the microscopic scale. One of my goals is to understand and model both micro-swimmers, and the even more microscopic mechanisms enabling them to swim. I have an interest in various types of micro-swimmers, ranging from living ones such as bacteria, algae or spermatozoa, to mathematical toy-models. More broadly, I like learning more about optimizing and controlling these systems, in particular linked to creating micro-robots with medical applications. When it comes to the numerical aspect, I perform and optimize computationally expensive simulations on larger-scale problems applied to physics as well, such as wireless power transfer for electric vehicles. Moreover, the methods used in this last aspect of my work are also widely applicable to fluid-structure simulations for micro-swimmers.

Publications

2024

  • J. Levillain, F. Alouges, A. DeSimone, A. Choudhary, S. Nambiar and I. Bochert. A bi-directional low-Reynolds-number swimmer with passive elastic arms [Preprint].

2023

  • F. Alouges, A. Lefebvre-Lepot, J. Levillain. A limiting model for a low Reynolds number swimmer with N passive elastic arms , May 2023. [PDF]

2020

  • J. Levillain. Hierarchical matrices and Adaptive Cross-Approximation, DENERG, Politecnico di Torino (Report, pre-doctoral research year). [PDF]

Communications

2024

  • 04/15/2024: Séminaire de l'équipe CALISTO, INRIA Université Côte D'Azur, Sophia Antipolis, France.
  • 03/20/2024: Séminaire des doctorants du LAMFA, LAMFA, Amiens, France.
  • 01/17/2024: Journée Maths en herbe (seminar for undergraduates), FMJH, talk Introduction to micro-swimming. IHES, Bures-sur-Yvette, France.

2023

  • 09/25/2023: Le Congrès des Jeunes Chercheurs en Mathématiques et Applications 2023, talk Bi-directional low-Reynolds-number swimmer models. CentraleSupéléc, Gif-sur-Yvette, France.
  • 08/30/2023: Talk at [ RIMS Fluid Dynamics Workshop ], Kyoto, Japan.
  • 08/22/2023: ICIAM 2023, mini-symposium on "Low-Reynolds-number swimming: modelling, analysis and applications", Tokyo, Japan. Talk and co-organization of MS with C. Moreau.
  • 07/05/2023: XX Jacques-Louis Lions Spanish-French School on Numerical Simulations in Physics & Engineering, poster presentation, Barcelona, Spain.
  • 06/16/2023: AJS Seminars, SISSA, Trieste, Italy. [Abstract]
  • 01/25/2023: Séminaire des doctorants du CMAP et du CMLS, École polytechnique, Palaiseau, France.

2022

  • 10/26/2022: RIMS Fluid Dynamics Group seminar, Kyoto University, Japan.
  • 10/18/2022: Microscale Ocean Biophysics online seminar.
  • 09/21-23/2022: Le Congrès des Jeunes Chercheurs en Mathématiques et Applications 2022, Calais, France. A mathematical model of flagellar activation mechanisms.
  • 06/13-17/2022: CANUM 2020+2, Flagellar Locomotion of Micro-organisms, invited by L. Giraldi and P. Lissy (Mini-symposium). [PDF]

Teaching

2023 -2024: École polytechnique

  • MAP350: Preparatory mathematics course, 1st year of Ingénieur Polytechnicien Program
  • Numerical Analysis 2: Linear Algebra and Optimization (MAA251, Bachelor of Science, 2nd year)

  • 2022 - 2023: École polytechnique

  • MAP350: Preparatory mathematics course, 1st year of Ingénieur Polytechnicien Program
  • Numerical linear algebra (MAA208, Bachelor of Science, 2nd year)
  • Supervision of various Bachelor Thesis (internships, Bachelor of Science, 3rd year)

  • 2021 - 2022: École polytechnique

  • Computational mathematics (MAA106, Bachelor of Science, 1st year)
  • Numerical linear algebra (MAA208, Bachelor of Science, 2nd year)
  • Supervision of various Bachelor Thesis (internships, Bachelor of Science, 3rd year): "Introduction to image denoising: on BM3D", "On the Perron-Frobenius theorem: discovering Google's PageRank algorithm".

  • Previous teaching experiences

      2020-2021
    • Tutoring in Mathematics for students pursuing a Bachelor of Science at Institut Villebon-Charpak, Université Paris-Saclay.
    • 2018-2019
    • Guest teacher in mathematics for high-schoolers at INSEP.
    • 2014-2018
    • Committee director and organizer of Model United Nations for high-schoolers via IMUNA.
    • 2012-2015
    • Tutoring in Mathematics, English and all subjects for middle- and high-schoolers at Lycée Notre Dame de la Providence.

    Miscellaneous

    Administrative work

    • PhD student representative at CMAP lab council (2022-2024).

    Climbing