Corentin Le Bihan

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ULB's Analysis seminar

Biographie

Portrait de Corentin Le Bihan
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Post Doc

Since October 2023 I have a postdoctoral position at the Université Libre de Bruxelles (under the supervision of Mitia Duerinckx). Before I was a PhD Student at ÉNS DE LYON (under the supervision of Sergio Simonella and Laure Saint-Raymond).

Interest

  • Partial differential equation
  • Kinetic theory
  • Equation of Boltzmann, Landau and Lenard Balescu
  • Large particle system

Éducation

  • Bachelor and master degree at the ÉNS de Lyon
  • PhD under the supervision of Sergio Simonella and Laure Saint Raymond

Ressearch interest

    My main interests (for the moment) are the derivation of kinetic equation from many body particles systems. In particular I want to understand the apparition of irreversibility in determinisitic system.

    During my PhD I worked on low density limits. The particles can interact only at short distance but very strongly. Hence each collision mix a little bit the system. The typical example of such system is a large billard of N hard identical spheres, each of of diameter ε. The interesting ratio between ε and N is Nε2 = 1 (when we are in dimension 3). When the number of particles goes to infinity the system is discribe by the Boltzmann equation.

    Now I work on an other interesting example is the mean-field system: the particles interact at long distance (of size 1) but weakly (the straigth of the interaction is of order 1/N). If you look at these system on time of order 1, it stays reversible (it describe by the Vlasov equation). However due to the mixing effects, the system becomes irreversible on long time (of order N). The system may be described by the Lennard-Balescu equation.

Analysis and PDEs seminar - ULB

Research

Publications

2025

Lenard-Balescu thermalization: rigorous derivation from a toy model, with M. Duerinckx Around the Quantum Lenard-Balescu equation

2024

Long time validity of the linearized Boltzmann uncut off and the linearized Landau equations from the Newt on Law, (accepté dans Communications on Pure and Applied Mathematics)

2022

The grazing collisions limit from the linearized Boltzmann equation to the Landau equation for short range potentials, with R. Winter (Kinetic and Related Models, 16, No. 5, 654 675 (2023))
Long time validity of the linearized Boltzmann equation for hard spheres: a proof without billiard theory, (Arch. Ration. Mech. Anal. 249, No. 4, Paper No. 40, 72 p. (2025))

2021

Boltzmann Grad limit of a hard sphere system in a box with isotropic boundary conditions, (Discrete and Continuous Dynamical Systems 42 , No. 4, 1903 1932)

2020

On essential selfadjointness of differential operators on closed manifolds, with Y.Colin de Verdière (Annales de la faculté des sciences de Toulouse, Math. (6) 31, No. 5, 1287 1302)

Manuscript of thesis

Effets de bord et comportement en temps long en théorie cinétique collisionnelle

Research talk

Janvier 2026

Séminaire de l'équipe EDP et physique mathématique de l'IMB, (Bordeau)

Décembre 2025

Workshop de l'équipe Analyse-EDP de l'ULB, (Spa)

October 2025

Séminaire d'Analyse et EDPs du LMJL, (Nantes)

Juanary 2025

Séminaire d'Analyse et EDPs de l'ULB, (Université Libre de Bruxelles)

March 2023

Conference "Scaling limits and generalized hydrodynamics", (GSSI, L'Aquila)

Juanary 2023

Seminario di Fisica Matematica (Sapienza Università di Roma)

June 2022

PhD Students Seminar, (ENS Lyon)

November 2022

Oberseminar Analysis (University of Bonn)

June 2022

PhD Students Seminar, (ENS Lyon)

June 2021

Team seminar at Basel University

October 2020

Séminaire compréhensible, Institue Fourrier (Grenoble)

Enseignement

2025 - 2026 à l’ULB :

TP d'intégration - mesure (automne 2025)

TP1 : σ-algèbres et mesures TP2 : Fonctions mesurables TP3 : Intégrale abstraite de Lebesgue TP4 : Comparaison entre les intégrales de Riemann et Lebesgue TP5 : Intégrale de Lebesgue TP6 : Ensembles pathologiques TP7 : Théorèmes d’extension de mesures Correction TP7 : Théorèmes d’extension de mesures TP8 : Théorèmes de Fubinni TP9 : Modes de convergence TP10 : Espaces de Lebegues TP11 : Théorème de Radon-Nikodym

TP d'analyse fonctionnelle (automne 2025)

TP1 : Topologie, espace vectoriel normé, Ascoli et Arzela TP2 : Topologie faible et faible étoile TP3 : Théorie spectral TP4 : Espace de Sobolev

2020 - 2023 à l’ENS Lyon :

Cours et TD d'analyse pour l'agrégation (automne 2022)

TD Evn, Baire et Banach Distributions Convexité Rudiments d’EDO 1 Rudiments d’EDO 2 Rudiments d’EDO 3

M1 Analyse avancée TD Cours assurés par Julien Vovelle (Automne 2021)

TD 1: Topology issues in product spaces and Banach spaces TD 2: L p compactness and Banach spaces TD 3: Hahn Banach theorem and locally convex topological vector spaces TD 4: Geometric Hahn Banach theorem and Fréchet spaces TD 5: Weak topology TD 6: Weak-∗ topology TD 7: Reflexivity TD 8: Distributions TD 9: Convolution of distributions TD 10: Tempered distribution TD 11: Sobolev spaces TD 12: Sobolev spaces and PDEss
M1 Analyse avancée TD Cours assurés par Laure Saint Raymond (Automne 2020)