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Xavier Erny
Postdoctoral researcher

Office: 05:3005
Email: xavier.erny@polytechnique.edu
Phone: +33643504316
Orcid ORCID iD iconhttps://orcid.org/0000-0002-3960-4085

About me CV
I am a postdoctoral researcher at Ecole Polytechnique (CMAP) working with Sylvie Méléard and Vincent Bansaye. The subject of the postdoc consists in elaborating and analyzing a model of hematopoietic stem cell regulation tu study the emergence of some types of cancer (myeloproliferative syndromes). We work in collaboration with Stéphane Giraudier (Hôpital Saint-Louis) and Evelyne Lauret (Institut Cochin).
I have done my PhD thesis at Université d'Evry (LaMME) under the supervision of Dasha Loukianova (Université d'Evry, LaMME) and Eva Löcherbach (Université Paris 1, SAMM). My thesis was dedicated to the study of large scale limit of (stochastic) particle systems in a diffusive regime, and particularly for systems with Hawkes-type dynamics.
I am more generally interested in applications of mathematics and computer science to model biological phenomena.

Research themes 
Interacting particle systems, nonlinear multivariate Hawkes processes, mean field limits, propagation of chaos, Point processes, Poisson measures, McKean-Vlasov equations, Random environment, Birth-death processes, Invasion model

Preprints 
  •  [9] V. Bansaye, X. Erny, S. Méléard (2022)
      Sharp approximation and hitting times for stochastic invasion processes.
       Submitted. ArXiv link
  •  [8] X. Erny (2022)
      Annealed limit for a diffusive disordered mean-field model with random jumps.
       In revision at Annales de l'Institut Henri Poincaré, Probabilités et Statistiques. ArXiv link
Publications 
  •  [7] X. Erny, E. Löcherbach, D. Loukianova (2021)
      Strong error bounds for the convergence to its mean field limit for systems of interacting neurons in a diffusive scaling.
      Accepted at Annals of Applied Probability. ArXiv link
  •  [6] X. Erny (2022)
      Mean field system of a two-layers neural model in a diffusive regime.
       Math. Neurosci. Appl. August 25, 2022. ArXiv link, MNA link
  •  [5] X. Erny, E. Löcherbach, D. Loukianova (2022)
      White-noise driven conditional McKean-Vlasov limits for systems of particles with simultaneous and random jumps.
      Probab. Theory Relat. Fields 2022. ArXiv link, PTRF link
  •  [4] X. Erny (2022)
       Well-posedness and propagation of chaos for McKean-Vlasov equations with jumps and locally Lipschitz coefficients.
       Stochastic Process. Appl. 150 192 - 214, August 2022. ArXiv link, SPA link
  •  [3] X. Erny, E. Löcherbach, D. Loukianova (2022)
      Mean field limits for interacting Hawkes processes in a diffusive regime.
       Bernoulli 28 (1) 125 - 149, February 2022. ArXiv link, Bernoulli link
  •  [2] X. Erny (2021)
      A convergence criterion for systems of point processes from the convergence of their stochastic intensities.
       Electron. Commun. Probab. 26 1 - 10, 2021. ECP link
  •  [1] X. Erny, E. Löcherbach, D. Loukianova (2021)
       Conditional propagation of chaos for mean field systems of interacting neurons.
       Electron. J. Probab. 26 1 - 25, 2021. EJP link

Talks 
  •   Summer School - Mean Field Model (Centre Henri Lebesgue) Campus Beaulieu, Rennes, 12-16 June 2023 : Annealed limit and quenched control for a diffusive disordered mean-field model with random jumps. Slides
  •   Groupe de travail Mathématiques financières et actuarielles, probabilités numériques au LPSM, 13 April 2023 : Conditional propagation of chaos for mean field particle systems. Slides
  •   Séminaire de Probabilités du MAP5 (Université Paris Cité), 10 March 2023 : Annealed and quenched limits for a diffusive disordered mean-field model with random jumps. Slides
  •   Séminaire de Probabilités et Statistiques de l'université de Nice, 31 January 2023 : Annealed limit for a diffusive disordered mean-field model with random jumps. Slides
  •   Séminaire de probabilités de l'IRMAR (Université de Rennes) 4 April 2022 : Strong error bounds for the conditional propagation of chaos for mean field systems of neurons. Slides
  •   Séminaire du département DATA (Université de Grenoble, LJK) 17 February 2022 : Strong error bounds for the conditional propagation of chaos for mean field systems of neurons. Slides
  •   Journées MAMOVI, 14 December 2021 : Conditional propagation of chaos for mean field system of interacting neurons. Slides
  •   Journée d'accueil des post-doctorants franciliens, 20 October 2021 : Particle system with random interaction. Slides
  •   International Conference in Mathematical NeuroScience 2021 (ICMNS 2021, online) 28 June 2021 : Conditional propagation of chaos for mean field system of neurons. Video. Slides
  •   Séminaire SAMM (Université Paris 1 Panthéon Sorbonne, SAMM) 5 February 2021 : Conditional propagation of chaos for mean field systems of interacting neurons. Slides
  •   Séminaire PMF (Université d'Evry, LaMME) 7 January 2021 : Conditional propagation of chaos for mean field systems of interacting neurons. Slides
  •   Groupe de travail PEIPS (Ecole polytechnique, CMAP) 12 November 2020 : Conditional propagation of chaos for mean field systems of interacting neurons. Slides
  •   Journées des Probabilités 24-28 June 2019 : Mean field limits for Hawkes processes in a diffusive regime. Slides
  •   Les Probabilités de Demain 14 June 2019 : Mean field limits for Hawkes processes in a diffusive regime. Video

Posters 
  •   International Conference on Mathematical Neuroscience 2020 : Conditional propagation of chaos for mean field systems of interacting neurons. Poster

Reports/Thesis 
  •   PhD Thesis "Large scale limits for interacting particle systems with simultaneous jumps in diffusive regime". PhD thesis
  •   PhD Thesis defence, Université d'Evry, 30 June 2021. Slides
  •   Master thesis "Limite de grande échelle de processus de Hawkes" (Sorbonne Université). Master thesis
  •   Internship report "Modélisation thermodynamique des réseaux de régulation de gènes" (Ecole Normale Supérieure Paris-Saclay 2A). Internship report
  •   Internship report "Les algorithmes de type Monte Carlo Tree Search appliqués aux Processus de Décisions Markoviens" (Ecole Normale Supérieure Paris-Saclay 1A). Internship report

Teaching 

    Agrégation
Agrégation externe de Mathématiques option D (Computer Science), rank: 98 (year: 2017)
list (non-exhaustive) of "développements": Développements
    Teaching at Université Paris 1 Panthéon-Sorbonne 
2022-2023: Teaching assistant, Statistics (L2 Mathematics). 30h. TDs
    Teaching at Ecole Polytechnique 
  •   2022-2023: Teaching assistant, Probability (equivalent L3 Mathematics). 22h.
  •   2021-2022: Teacher for the last session of the course "Mathematical modelling in neurosciences" of the master MSV. 3h. Course outline
    Teaching at Université d'Evry 
  •   2020-2021: Teaching assistant, Methodology (L1 Mathematics-Computer Science). 6h. Support
  •   2020-2021: Teaching assistant, Probability (L2 Physics). 18h. TD1 TD2 TD3 TD4 TD5 TD6 TD7 TD8 TD9
  •   2020-2021: Teaching assitant, Probability (L2 Mathematics). 39h. TD1 TD2 TD3 TD4
  •   2018-2020: Teaching assistant, Probability (L2 Mathematics/L2 Computer science). 39h. TD1 TD2 TD3 TD4
  •   2018-2020: Teaching assistant, Probability (L1 Biology). 15h. TDs
  •   2018-2020: Oral examiner, Algebra and Analysis (L1 Mathematics). 10h. Exercices d'analyse, Exercices d'algèbre
    Teaching at Lycée Saint-Louis
2017-2018: Oral examiner, Mathematics (MPSI). Divers, Continuité, Dérivation, DL, Taylor, Intégration, Séries, Polynômes, Fractions rationelles, EDO, Matrices, Espaces vectoriels, Déterminant, Espaces euclidiens