I am interested in groups and geometry from an operator algebraic viewpoint. I especially like questions like:
What can we say about groups, directed graphs, varieties, dynamical systems, and other geometrical objects from related operator algebras?
When are interesting geometric phenomena just shadows of natural noncommutative concepts?
I also really like noncommutative versions of well-known theories and objects, such as multidimensional analytic function theory (nc function theory), Choquet theory (boundary representations), and dynamical topological and measure spaces (dynamical C*- and von-Neumann algebras).