I am working in the field of Stochastic analysis, Functional inequalities and Optimal transport. My main theme of research is the use of Malliavin, semigroup and optimal transport techniques to study functional inequalities and limit theorems for probabilistic infinite dimensional models. Namely I combine techniques from:
- Stochastic analysis for random measures.
- Random point processes and stochastic geometry.
- Malliavin-Stein approach and limit theorems.
- Functional inequalities for Markov semigroups à la Bakry-Emery.
- Transport inequalities, concentration of measure, log-Sobolev type inequalities.
- Heat kernels, Laplace operators and Ricci curvature on graphs and sub-Riemannian manifolds.
More broadly, I am also interested with many aspects of modern probability such as free probability, rough paths, regularity structures, SPDEs, random geometry, interacting particle systems and their interplays with my field of expertise.