I am working in the field of Stochastic analysis, Functional inequalities and Optimal transport.
My main focus is the use of *optimal transport* and *functional inequalities* to study probabilistic models from statistical physics or mechanics, mostly *point processes* and *Liouville quantum gravity measures*.

More specifically, I am interested in:

- Stochastic analysis and optimal transport for particle systems.
- Transport inequalities and concentration of measure.
- Functional inequalities for Markov semigroups à la Bakry-Emery.
- Heat kernels, Laplace operators and Ricci curvature on non-smooth spaces.
- Liouville quantum gravity measures in arbitrary dimension.
- Malliavin-Stein approach and limit theorems.

More broadly, I am also interested with many aspects of modern probability such as free probability, rough paths, regularity structures, SPDEs, random geometry, percolation and their interplays with my field of expertise.