My interest is primarily the topology of 3-dimensional manifolds. In particular I am interested in the theory of the Heegaard structure of these manifolds as a mean of understanding their topology. This approach includes various aspects of group theory such as Nielsen equivalence of generating systems of their fundamental groups and groups in general. This led to classifications of Heegaard splittings of Seifert fibered spaces and a structure theorem for Heegaard splittings of Hyperbolic manifolds. Research in other directions included the existence of closed incompressible surfaces in 3-manifolds. In particular those who have infinitely many irreducible Heegaard splittings.
Recently I am looking at the curve complex associated with a Heegaard surface and at its disk sub-complexes determined by a Heegaard splitting. The curve complex allows one to study all Heegaard splittings of a given genus and deal with various questions of ''generic'' behavior of these splittings.