My research interests are in 3-dimensional topology and geometry, knot theory, hyperbolic geometry,
quantum topology and combinatorics. In the recent years I have been interested in exploring the
interplay and relations between physics originated and combinatorial 3-manifold invariants, and
geometric structures on 3-manifolds coming from the Thurston geometrization picture. For instance,
I have been studying relations between quantum knot invariants, such as the Jones polynomial,
and geometric structures of knot complements such as hyperbolic geometry and incompressible surfaces.