I work mainly in general topology and set-theoretic topology. General topology might be defined as the study of limit processes in various settings (e.g., metric space, or more abstract spaces) and set-theoretic topology might be defined as part of the foundations of mathematics involving the interaction of modern set-theory (including descriptive set theory), logic and topology, and to a lesser extent, measure theory. Much work has been done on foundation of point-set topology and general topology, but results reach to most areas of topology. Most recently in general tropology I have worked on hyperspaces, and in set-theoretic topology on remainders of Stone-Cech compactifications.
I am interested in large-scale topological invariants of infinite groups. A finitely generated group with a specified generating set carries a natural metric called the word metric. This turns the algebraic object into a geometric one. Since different choices of generating sets yield distinct metrics, the correct approach is to consider all such metrics equivalent and to focus on the topological properties of the space that are invariant of small changes. I am particularly interested in properties relating to large-scale coverings and notions of dimension. I work on asymptotic dimension and related notions as well as G. Yu's property A.