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

My research focuses on the study of micro-swimmers: living ones such as bacteria, algae or spermatozoa, but also toy-models. I study these systems as a whole, from trying to understand and modelize, using partial differential equations and numerical methods, the mechanisms that enable them to swim. I am also interested in their controllability.

Communications

2023

  • 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: CJC-MA, Calais, France. A mathematical model of flagellar activation mechanisms.
  • 06/13-17/2022: Flagellar Locomotion of Micro-organisms, CANUM 2020+2, invited by L. Giraldi and P. Lissy (Mini-symposium). [PDF]

Publications

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]

Teaching

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 from November 2022.

    Climbing