- Singular SPDEs
- Paracontrolled calculus
- Stochastic Quantization
- Variational methods
PhD in Mathematics
University of Rennes
Masters degree in Pure Mathematics
University of Rennes
Agrégation de Mathématiques
ENS Rennes
- 2024, Young researchers in deterministic and probabilistic dispersive equations, EPFL, Lausanne
- 2024, Turbulent.e.s, Ecole Polytechnique
- 2024, Journées EDP Auvergene-Rhône-Alpes, LJK Grenoble
I am mostly interested in the study of singular SPDEs using the tools from paracontrolled calculus. I defended my PhD thesis “Anderson stochastic quantization and paracontrolled calculus : stochastic PDEs in a singular environment.” in June 2024. Some of the results obtained during my PhD include:
- a fine comparison property between the Green functions of the Anderson Hamiltonian and the usual Laplace Beltrami operator;
- a variational construction of an invariant measure to the polynomial $\Phi_2$ model driven by the Anderson operator;
- a global solution theory for the same model starting from deterministic rough data;
- probabilistic properties of the dynamics (still a work in progress though).
Starting from September 2024, I work on related topics at UMPA, ENS Lyon, under the supervision of Nikolay Tzvetkov.
Non-local quasilinear singular SPDEs 2024
We study a counterpart to the quasilinear generalized parabolic Anderson model on the 2-dimensional torus where the coefficients are nonlocal functionals of the solution.
Anderson stochastic quantization equation 2024
H. Eulry - A. Mouzard - T. Robert
We study the parabolic defocusing stochastic quantization equation with both mutliplicative spatial white noise and an independant space-time white noise forcing, on compact surfaces, with polynomial nonlinearity.
Variational methods for some singular stochastic elliptic PDEs 2022
I. Bailleul - H. Eulry - T. Robert
We use some tools from nonlinear analysis to study two examples of singular stochastic elliptic PDEs that cannot be solved by the contraction principle or the Schauder fixed point theorem.
- January 2024, Nicolas Perkowski’s team seminar, Freie Universität, Berlin.
- October 2023, Landau seminar, IRMAR, Rennes.
- October 2023, ANR Smooth Workshop, Institut Elie Cartan de Lorraine, Nancy.
- October 2022, Nicolas Perkowski’s team seminar, Freie Universität, Berlin.
- May 2022, ”Rough paths, stochastic partial differential equations and related topics” seminar, Technische Universität, Berlin.