I work on geometry, dynamical systems, and operator algebras. In other words, the study of spaces and the influence their geometry has on symmetry groups and operator algebras associated with them. Specifically, my recent achievements are concerned with geometric group theory (e.g. L2 cohomology, intermediate rank), nonpositively curved spaces (e.g. Bruhat-Tits buildings, polyhedral complexes of friezes),

foliation theory (e.g. concentration of transverse measures), and noncommutative geometry (e.g. property RD, Baum-Connes).