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.

Selected Publications

Crosscap numbers and the Jones polynomial, w. Lee, Advances in Mathematics, 286, 308-337(2016).

Hyperbolic semi-adequate links, w. Futer and Purcell, Communications in Analysis and Geometry, Vol 23, No 5, 991-1028(2015).

Knot Cabling and the Degree of the Colored Jones Polynomial, w. Tran, New York Journal of Mathematics, Volume 21, 905-941(2015).

Quasifuchsian state surfaces, w. Futer and Purcell, Transactions of the American Math. Soc., Vol 366, Issue 8, 4323-4343 (2014).

Guts of surfaces and the colored Jones polynomial, w. Futer and Purcell, Research Monograph, Lecture Notes in Mathematics, Vol. 2069, xii+ 175p., Berlin, Springer (2013).

Cosmetic crossing changes of fibered knots, J. Reine Angew. Math., Vol 2012, Issue 669, 151-164.

An intrinsic approach to invariants of framed links in 3-manifolds, Quantum Topology, Vol 2, Issue 1, 71-96 (2011).