Broadly speaking, my research focuses on group theory. I am particularly interested in combinatorial, geometric, and dynamical properties of countable groups, as well as certain connections with operator algebras and Polish groups.
In my recent work, I am particularly interested in (discrete or topological) high transitivity , (dense) embeddings in certain Polish groups, and the properties of the space of subgroups (of a countable group G) and the dynamical system obtained when G acts by conjugation. In the past, I have worked on large-scale geometric properties such as coarse embeddings in Hilbert spaces or weak forms of amenability such as the Haagerup property and inner amenability, as well as on the space of marked finitely generated groups.
My favorite groups are those acting on trees, in particular free groupes and Baumslag-Solitar groups, and wreath products.
I often work with combinatorial objects like graphs, spaces with walls, cubical complexes, etc. I also use analytical tools, among which the Baire category theorem is one of my favorites.