Léo Vivion I am currently post-doc at the Laboratoire de Mathématiques Pures et Appliquées of the Université du Littoral Côte d'Opale (France), where I work with Mélodie Andrieu and Shalom Eliahou.

e-mail: lvivion.math [at] gmail.com

My scientific interests lie in dynamics, in a broad sense. I completed my PhD thesis in Partial Differential Equations, and since 2021-2022, I have developed an interest in the study of dynamical systems from a 'discrete mathematics' perspective. This has led me to develop a taste and expertise in Symbolic Dynamics and Combinatorics on Words.

• Combinatorics on Words. Billiards. Various notions of complexities. Balance. Numeration systems.
  
  
• PDE analysis. Kinetic equations, Vlasov-like equations, Landau damping. Mean field limit, semi-classical limit. Shrödinger-like equations, solitary waves, quantum dissipative systems.

International Conferences with selection committees

• L. Vivion, On the k-binomial complexity of hypercubic billiard words, Mons theoretical computer science days, 2024
• M. Andrieu and L. Vivion, An abelian renormalization, Mons theoretical computer science days, 2024
• M. Andrieu and L. Vivion, Imbalances in hypercubic billiard words (II), Mons theoretical computer science days, 2024
• M. Andrieu and L. Vivion, Minimal complexities for infinite words written with d letters, Invited paper, Combinatorics on words, 14th international conference, Springer, 3-13, 2023
• M. Andrieu and L. Vivion, Imbalances in hypercubic billiard words, Mons theoretical computer science days, 2022

Papers in progress

• M. Andrieu, S. Eliahou and L. Vivion, A normality conjecture on rational base number systems.
• M. Andrieu and L. Vivion, Characterization of imbalances in hypercubic billiard words (journal version).
• M. Andrieu and L. Vivion, Abelian complexity of hypercubic billiard words (journal version).
• M. Andrieu and L. Vivion, An abelian renormalization process on infinite words (journal version).
• L. Vivion, On the k-binomial complexity of hypercubic billiard words (journal version).

Articles published in peer-reviewed journals

• T. Goudon and L. Vivion, On quantum dissipative systems: ground states and orbital stability, Journal de l'Ecole Polytechnique -- Mathématiques, Volume 10, 447-511, 2023
• T. Goudon and L. Vivion, Landau damping in dynamical Lorentz gases, Bulletin de la SMF, 149(2), 237-307, 2021
• T. Goudon and L. Vivion, Numerical investigation of solitary waves stability for quantum dissipative systems, Journal of Mathematical Physics, 62(1), 2021
• T. Goudon, and L. Vivion, Numerical investigation of Landau damping in dynamical Lorentz gases, Phys. D., 403, 2020

• 2024-now: Post-doctoral position under the supervision of Mélodie Andrieu, LMPA, Univeristé du Littoral Côte d'Opale, Calais.
  
  
• 2021-2023: ATER (teaching position), I2M, Aix-Marseille Université, Marseille.
  
  
• 2020-2021: Post-doctoral position under the supervision of Daniel Han-Kwan, CMLS, Ecole Polytechnique, Palaiseau.
  
  
• 2017-2020: PhD student under the supervision of Thierry Goudon, LJAD, Université Côte d'Azur, Nice.
• PhD title: Classical and quantum particles interacting with their environment: stability analysis and asymptotic issues.
• PhD defense: September 8th, 2020.
• Manuscript and Slides.
  
  
• 2015-2017: Scholarship at ENS Rennes and Master's degree in mathematics at Université Nice Sophia Antipolis.

2021-2023: ATER (196h/year)

• Analysis (series, integration, DLs), cours + TD, L2.
• General Mathematics (algebra and analysis), cours + TD, L1 et Année de Mise à Niveau Scientifique.
• Khôlles (linear algebra, integration, group theory), L2 MPCI.
  
  

2020-2021: Vacations for the Bachelor of the Ecole Polytechnique (teaching in english, 56h)

• Analysis (integration, ODE, parametric curves), TD, L1.
  
  

2017-2020: PhD with teaching duties (64h/year)

• Descriptive statistics, TD, L1.
• Linear algebra, TD, L1 and L2.
• Analysis, TD, L1.
• Analysis and optimization, TD, L1.
• Khôlles.

• MATh.en.JEANS congress, Université du Littoral Côte d'Opale, 2024.
• Fête de la science (science festival), Université du Littoral Côte d'Opale, 2024.
• Fête de la science (science festival), Platonic solid et Construction of a giant fractal, Université Côte d'Azur, 2019.
• Fête de la science (science festival), Mathematical escape game, Université Côte d'Azur, 2018.

• Coordinator of the PEPS JCJC (First support exploratory project for young researchers) A link between two notions of complexity for symbolic dynamical systems, 2024.
• PhD student representative (elected) at the doctoral school Sciences Fondamentales et Appliquées, Université Côte d'Azur, 2019-2020.