Biography

I am Maitre de Conférences (~ Associate Professor) at Université Claude Bernard Lyon 1.

My research focuses on problems originating from physics in which a stochastic component plays a key role. This randomness mostly originates from molecular behaviors, such as inter-collisions and interactions with the boundary in kinetic theory, from some extra microstructure, or from diffusive effects when studying nonlinear diffusions. Mathematically, the tools I use come mainly from probability theory (Harris theorem, coupling techniques, stochastic calculus) and from the theory of partial differential equations.

Before moving to Lyon, I was a Civis3I Postdoctoral Fellow (part of the MSCA action) at University La Sapienza, under the supervision of Alessandra Faggionato. Before that, I was a postdoc researcher at the LJLL (Sorbonne Université), under the supervision of Mitia Duerinckx (FNRS) and Antoine Gloria (LJLL, SU). I studied for my PhD at the LPSM (Sorbonne Université) under the supervision of Nicolas Fournier (LPSM, Sorbonne Université) and Stéphane Mischler (CEREMADE, Université Paris Dauphine).

Interests

Kinetic theory and boundary effects;
Nonlinear diffusions;
Mean-field limits;
Stochastic homogenization.

Education

CIVIS3i Postdoctoral fellow, 2022-2023

Sapienza Università di Roma
Postdoctoral Researcher, 2021-2022

LJLL, Sorbonne Université
PhD in Applied Mathematics, 2017-2020

LPSM, Sorbonne Université
MASt in Mathematics, 2017

University of Cambridge
Ingénieur Statisticien, 2017

ENSAE ParisTech

Preprints and Publications

(2023). A.Bernou : Asymptotic Behavior of Degenerate Linear Kinetic Equations with Non-Isothermal Boundary Conditions. Preprint.

PDF arXiv HAL

(2023). A.Bernou & Y. Liu: Path-dependent McKean-Vlasov equation: strong well-posedness, propagation of chaos and convergence of an interpolated Euler scheme. Preprint.

PDF arXiv HAL

(2022). A.Bernou, M. Duerinckx & A. Gloria: Homogenization of Active Suspensions and Reduction of Effective Viscosity. Preprint.

PDF arXiv HAL Some slides

(2022). A.Bernou, K. Carrapatoso, S. Mischler & I. Tristani: Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition. Ann. Institut Henri Poincaré - Analyse Non Linéaire, published online.

PDF DOI arXiv

(2022). A.Bernou: Convergence Towards the Steady State of a Collisionless Gas With Cercignani-Lampis Boundary Condition. Communications in Partial Differential Equations, 47:4, 724-773.

PDF arXiv Poster DOI

(2022). A.Bernou & N.Fournier: A Coupling Approach for the Convergence to Equilibrium for a Collisionless Gas. Annals of Applied Probability, 32(2): 764:811.

PDF Project Euclid arXiv Some slides (in French) Some slides (in English)

(2022). A.Bernou: On Subexponential Convergence to Equilibrium of Markov Processes. Séminaire de Probabilités LI.

PDF arXiv Some Related Slides DOI

(2020). A.Bernou: A Semigroup Approach to the Convergence Rate of a Collisionless Gas. Kinetic and Related Models, 13(6): 1071-1106.

PDF DOI arXiv Poster

(2020). Ph.D. Thesis: Long-Time Behavior of Kinetic Equations with Boundary Effects. Supervisors: Nicolas Fournier (LPSM) and Stéphane Mischler (CEREMADE). Defended in December, 2020.

PDF Slides

Talks

I will be next in :

Séminaire du LSAF, Lyon, January 2024;
Séminaire Analyse des EDP et modélisation, ENS Lyon, February 2024;

Some former talks (see the complete list for more):

How to simulate path-dependent McKean-Vlasov equations ?, 43rd Conference on Stochastic Processes and their Applications, Lisbon, August 2023.
Beyond the mean-field limit : uniform in time estimates for the cumulants, Seminario de Probabilidades de Chile, Centro de Modelamiento Matem'atico, Santiago, April 2023.
On the Cercignani-Lampis boundary condition in kinetic theory, Workshop du projet ANR EFI, Lyon, November 2022.
Beyond the mean-field limit for the McKean-Vlasov particle system : Uniform in time estimates for the cumulants, Workshop Metastability, mean-field particle systems and non linear processes, Université Jean Monnet, Saint-Etienne, May 2022. Slides
Superfluidity of a Hydrodynamic Model for Active Suspensions, Séminaire de Probabilités, Institut de Mathématiques de Marseille, January 2021. Slides
Asymptotic Behavior of Kinetic Equations with Boundary Conditions, Séminaire du CEREMADE Analyse-Probabilités, November 2021.