Charles Bertucci

Charles Bertucci

Welcome!

I am a CNRS researcher in Mathematics at the Applied Maths department of École polytechnique in Palaiseau, France. I defended my thesis on the 11th of December, 2018, and I defended my Habilitation à Diriger les Recherches in June of 2022.

I am also a part time teacher at École polytechnique since 2020. In addition, this year, I gave a Peccot Course. You can find more information here. Lecture notes of the course are available here.

With Yves Achdou, Jean-Michel Lasry and Pierre-Louis Lions, we organized the workshop Mean Field Games and Applications.

Download my resumé (in french, lastly updated 2024).

Interests
  • Analysis
  • PDE
  • Mean Field Games
  • Game theory
  • Probabilities
  • Numerical methods
  • Economics
  • Optimal Transport

Papers

  • [27] An approximation of the squared Wasserstein distance and an application to Hamilton-Jacobi equations, with Pierre-Louis Lions, arXiv preprint arXiv:2409.11793, 2024.
  • [26] Curvature in chemotaxis: A model for ant trail pattern formation, with Matthias Rakotomalala and Milica Tomasevic, arXiv preprint arXiv:2408.13363, 2024.
  • [25] Strategic geometric graphs through mean field games, with Matthias Rakotomalala, arXiv preprint arXiv:2404.13975, 2024. -[24] Noise through an additional variable for mean field games master equation on finite state space, with Charles Meynard, arXiv preprint arXiv:2402.05635, 2024.
  • [23] A spectral dominance approach to large random matrices: part II, with Jean-Michel Lasry and Pierre-Louis Lions, arXiv preprint arXiv:2402.16376, 2024.
  • [22] A two spaces extension of Cauchy-Lipschitz Theorem, with Pierre-Louis Lions, arXiv preprint arXiv:2402.19092, 2024.
  • [21] Agents’ Behavior and Interest Rate Model Optimization in DeFi Lending, with Louis Bertucci, Mathis Gontier Delaunay, Olivier Gueant, and Matthieu Lesbre, available at SSRN 4802776,2024.
  • [20] Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measures, 2023, arXiv preprint arXiv:2306.04283.
  • [19] On Lipschitz solutions of mean field games master equation, with Jean-Michel Lasry and Pierre-Louis Lions, Journal of Functional Analysis, 287(5), 110486, 2024.
  • [18] A mean field model for the development of renewable capacities, with C. Alasseur, M. Basei and A. Cecchin, Mathematics and Financial Economics, 17(4), 695-719, 2023.
  • [17] A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem, 2022 with Jean-Michel Lasry and Pierre-Louis Lions, arXiv:2210.02780, 2022.
  • [16] A spectral dominance approach to large random matrices, with Mérouane Debbah, Jean-Michel Lasry and Pierre-Louis Lions, Journal de Mathématiques Pures et Appliquées, 164, 27-56, 2022.
  • [15] Mean field games master equations: from discrete to continuous state space, SIAM journal on Mathematical Analysis, 56(2), 2569-2610, with Alekos Cecchin, 2024.
  • [14] Mean field games with incomplete information, 2022 pdf
  • [13] On monotone solutions of mean field games master equations Séminaire Laurent Schwartz—EDP et applications, 1-13, 2021.
  • [12] Monotone solutions for mean field games master equations: continuous state space and common noise. Communications in Partial Differential Equations, 48(10-12), 1245-1285, 2023.
  • [11] Monotone solutions for mean field games master equations: finite state space and optimal stopping. Journal de l’École polytechnique—Mathématiques, 8, 1099-1132, 2021.
  • [10] How Resilient is the Bitcoin Protocol? Université Paris-Dauphine Research Paper, with L. Bertucci, J.-M. Lasry and P.-L. Lions, 2022.
  • [9] Mean Field Game Approach to Bitcoin Mining. SIAM Journal on Financial Mathematics, 15(3), 960-987, with L. Bertucci, J.-M. Lasry and P.-L. Lions, 2024.
  • [8] A class of short-term models for the oil industry addressing speculative storage. Finance and Stochastics, 26(3), 631-669, with Y. Achdou, J.-M. Lasry, P.-L. Lions, A. Rostand and J. Scheinkman, 2022.
  • [7] Master equation for the finite state space planning problem. Archive for Rational Mechanics and Analysis, vol. 242, p. 327-342. with J.-M. Lasry and P.-L. Lions, 2021.
  • [6] Strategic advantages in mean field games with a major player, Comptes Rendus Mathématique, 58.2: 113-118. with J.-M. Lasry and P.-L. Lions, 2020.
  • [5] A remark on Uzawa’s algorithm and an application to mean field games systems. ESAIM: Mathematical Modelling and Numerical Analysis, vol. 54, no 3, p. 1053-1071, 2020.
  • [4] Transmit strategies for massive machine-type communications based on mean field games. Proceedings of the International Symposium on Wireless Communication System (ISWCS), with S. Vassilaras, J.-M. Lasry, G. Paschos, M. Debbah and P.-L. Lions, 2018.
  • [3] Some remarks on mean field games. Communications in Partial Differential Equations, vol. 44, no 3, p. 205-227 with J.-M. Lasry and P.-L. Lions, 2019.
  • [2] Fokker-Planck equations of jumping particles and mean field games of impulse control. Annales de l’Institut Henri Poincaré C, Analyse non linéaire, Vol. 37. No. 5. Elsevier Masson, 2020.
  • [1] Optimal stopping in mean field games, an obstacle problem approach. Journal de Mathématiques Pures et Appliquées, Volume 120, p 165-194, 2018.

Contact