Welcome to my webpage! I am currently professor in the Université de Bretagne Occidentale, France. My main reserch area is at the intersection of probability, geometry and mathematical physics. Recently I have mainly been working on problems involving rough paths, singular stochastic PDEs and Euclidean quantum field theories. I keep a particular interest in the study of hypoelliptic diffusions, including a class of diffusions intrinsically associated with any relativistic spacetime, called relativistic diffusions.

Click here for a brief CV (07/2023, in French). Click on the following links to find the webpages of my present or former PhD students Pierre Perruchaud, Antoine Mouzard, Hugo Eulry and Nicolas Moench.

Keywords

Euclidean quantum fields theories

Singular PDEs, paracontrolled calculus, regularity structures

Rough paths, mean field stochastic rough differential equations, rough dynamics on paths space, rough flows

Stochastic differental geometry, Lorentzian geometry

Sub-Riemannian geometry, Malliavin calculus

Particle systems, coupling method, nonlinear Markov processes

Scientific publishing -- The Annales Henri Lebesgue is a generalist journal of mathematics, fully open access and free of author charges. This non-profit journal is supported by public institutions. It publishes high-quality articles from any area of mathematics, from the most applied to the most abstract, with the aim of highlighting beautiful mathematical inventions.

Grants

• 2023-2028: P.I. of the ANR Grant SMOOTH on singular SPDEs and dispersive PDEs with random initial conditions.
• 2019-2022: Member of the GdR TRAG on rough paths theory and related topics.
• 2018-2021: Member of the GdR Renorm on renormalisation.
• 2017-2021: P.I. of the ANR Grant SINGULAR.
• 2011-2015: P.I. of the ANR Grant "Retour Post-doctorant", 11-PDOC-0025.

Two 2-year postdoc positions (2025-2027+) Funded by the ANR Grant Smooth, to work on singular stochastic PDEs or dispersive PDEs with low regularity initial conditions. To apply: send CV and project to Nikolay Tzvetkov and myself.

Our planet

Groupe de travail sur la situation ecologique de la planete.