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.