Office Hours

• Monday:12:45-1:30pm
• Wednesday:12:45-1:30pm
• Friday:12:45-1:30pm

Research Interests

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).