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.

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

Papers

  • Optimal stopping in mean field games, an obstacle problem approach. Journal de Mathématiques Pures et Appliquées 2018, Volume 120, p 165-194.
  • 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.
  • Some remarks on mean field games. Communications in Partial Differential Equations, 2019, vol. 44, no 3, p. 205-227 with J.-M. Lasry and P.-L. Lions.
  • Transmit strategies for massive machine-type communications based on mean field games. Proceedings of the International Symposium on Wireless Communication System (ISWCS), 2018 with S. Vassilaras, J.-M. Lasry, G. Paschos, M. Debbah and P.-L. Lions
  • A remark on Uzawa’s algorithm and an application to mean field games systems. ESAIM: Mathematical Modelling and Numerical Analysis, 2020, vol. 54, no 3, p. 1053-1071.
  • Strategic advantages in mean field games with a major player, 2020, Comptes Rendus Mathématique, 58.2 (2020): 113-118. with J.-M. Lasry and P.-L. Lions.
  • Master equation for the finite state space planning problem. arXiv preprint arXiv:2002.09330, 2020 with J.-M. Lasry and P.-L. Lions.
  • A class of short-term models for the oil industry addressing speculative storage. arXiv preprint arXiv:2003.11790, 2020 with Y. Achdou, J.-M. Lasry, P.-L. Lions, A. Rostand and J. Scheinkman.
  • Mean Field Game Approach to Bitcoin Mining. arXiv preprint arXiv:2004.08167, 2020 with L. Bertucci, J.-M. Lasry and P.-L. Lions.
  • How Resilient is the Bitcoin Protocol? Université Paris-Dauphine Research Paper, (3907822), with L. Bertucci, J.-M. Lasry and P.-L. Lions.
  • Monotone solutions for mean field games master equations: finite state space and optimal stopping. arXiv preprint arXiv:2007.11854.
  • Monotone solutions for mean field games master equations: continuous state space and common noise. arXiv preprint arXiv:2107.09531.
  • Mean field games with incomplete information, 2022 pdf
  • Mean field games master equations: from discrete to continuous state space, 2022 with Alekos Cecchin, arXiv preprint, arXiv:2207.03191.
  • A spectral dominance approach to large random matrices, 2022 with Mérouane Debbah, Jean-Michel Lasry and Pierre-Louis Lions, Journal de Mathématiques Pures et Appliquées, 164, 27-56.
  • A singular infinite dimensional Hamilton-Jacobi-Bellman equation arising from a storage problem, 2021 with Jean-Michel Lasry and Pierre-Louis Lions, arXiv:2210.02780, 2022 pdf
  • A mean field model for the development of renewable capacities, 2022 arXiv preprint arXiv:2210.15023, with C. Alasseur, M. Basei and A. Cecchin.
  • On Lipschitz solutions of mean field games master equation, 2023 with Jean-Michel Lasry and Pierre-Louis Lions, arXiv preprint arXiv:2302.05218,
  • Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measures, 2023, arXiv preprint arXiv:2306.04283.