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. More generally I have been studying relations between certain 3-dimensional TQFT structures and geometric structures 3-manifolds.
The material below is based on research partially supported by the
National Science Foundation since 1996.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
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