Probability theory, in particular:
- discrete and continuum random trees,
- scaling limits,
- branching processes,
and technical tools for dealing with such objects. Right now I am mainly working on Lévy forests and their representation as scaling limits of Galton-Watson R-forests, using measure-theoretic tools developed on somewhat general classes of measured rooted R-trees. I also have broader interests in other aspects of probability such as percolation, statistical mechanics, random walks, random geometry and stochastic processes.
Besides this I also have research interests in rough path theory and related areas, in particular in connection with signatures, randomized signatures and their interface with differential geometry.