Some research papers since 2008:
25. Kauffman bracket skein modules of small 3-manifold.
(with R. Detcherry and A. Sikora), Preprint 2023 PDF
24. Constructions of q-hyperbolic knots.
(with J. Melby), Preprint 2023 PDF
23. Pants complex, TQFT and hyperbolic geometry.
(with R. Detcherry), Preprint 2021 PDF
22. Volumes of fibered 2-fold branched covers of 3-manifolds
(with S. Hirose and E. Kin), Journal of Topology and Analysis, to appear. PDF
21. Alternating links on surfaces and volume bounds.
(with J. Purcell), Communications in Analysis and Geometry, to appear. PDF
20. Jones diameter and crossing number of knots.
(with C. Lee), Advances in Mathematics,vol. 417, Paper No. 108937(2023).
19. Cosets of monodromies and quantum representations.
(with R. Detcherry), Indiana Univ. Mathematics Journal, Vol 71, No 3, 1101-1129 (2022).
18. Growth of quantum $6j$-symbols and applications to the Volume Conjecture.
(with G. Belletti, R. Detcherry and T. Yang), Journal of Differential Geometry, 120(2), 199-229 (2022).
17. Guts, volume and Skein Modules of 3-manifolds
(with B. Bavier), Fundamenta Math,Vol 256, No 2, 195-220 (2022).
16. Gromov norm and Turaev-Viro invariants.
(with R. Detcherry), Ann.Sci. de l'Ecole Normale Super., Vol. 53, Fasc. 6, 1363-1391 (2020).
15. The Strong Slope Conjecture and torus knots.
Journal of the Math. Soc. of Japan, 72 no. 1, 73-79 (2020).
14. Quantum representations and monodromies of fibered links.
(with R. Detcherry), Advances in Mathematics, Volume 351, 676-701(2019).
13. Turaev-Viro invariants, colored Jones polynomial and volume.
(with R. Detcherry and T. Yang), Quantum Topology Vol. 9, Issue 4, 775-813(2018).
12. Geometric estimates from spanning surfaces. (with S. D. Burton),
Bulletin of London Math. Society, Vol. 49, Issue 4, 694-708(2017).
11. Crosscap numbers and the Jones polynomial. (with C. Lee),
Advances in Mathematics, 286, 308-337(2016).
10. Knot Cabling and the Degree of the Colored Jones Polynomial. (with A. T. Tran),
New York Journal of Mathematics, Volume 21, 905-941(2015).
9. Hyperbolic semi-adequate links. (with D. Futer and J. Purcell),
Communications in Analysis and Geometry, Vol 23, No 5, 991-1028(2015).
8. Quasifuchsian state surfaces. (with D. Futer and J. Purcell),
Transactions of the American Math. Soc., Vol 366, Issue 8, 4323-4343 (2014).
7. Guts of surfaces and the colored Jones polynomial. (with Futer and Purcell),
Research Monograph, Lecture Notes in Mathematics, Vol. 2069, x\~ 173p., Berlin, Springer (2013).
6. Cosmetic crossing changes of fibered knots.
J. Reine Angew. Math.(Crelle's Journal), Vol 2012, Issue 669, 151-164.
5. Cosmetic crossings and Seifert Matrices.
(with with C. Balm, S. Friedl and M. Powell),
Communications in Analysis and Geometry, Vol 20, No 2,235-254 (2012).
4. An intrinsic approach to invariants of framed links in 3-manifolds.
Quantum Topology, Vol 2, Issue 1, 71-96(2011).
3. Cusp areas of Farey manifolds and applications to knot theory. (with D. Futer and J. Purcell),
Int.Math. Res. Notices, Vol. 2010, Issue 23, 4434-4497 (2010).
2. Dehn filling, volume and the Jones polynomial. (with Futer and Purcell),
Journal of Differential Geometry, Vol 78, no 3, 429-464 (2008).
1. The Jones polynomial and graphs on surfaces (with O. Dasbach, D. Futer, X.-S. Lin and N. Stoltzfus),
Journal of Combinatorial Theory Ser. B , Vol. 98, Issue 2, 384-399(2008).
1. State Surfaces of Links.
Encyclopedia of Knot Theory, Chapter 24, in press (2020).
2. A survey of hyperbolic knot theory.
(with D. Futer and J. Purcell), Knots, Low-dimensional Topology and Applications,
Springer Proceedings in Mathematics & Statistics Vol. 284, 1-30(2019).
3. Jones polynomials, volume, and essential knot surfaces: A survey.
(with Futer and Purcell), in the Proceedings
of ``Knots in Poland ``, Warsaw, July 2010, Banach Cent. Pub. Vol 100, 51-77 (2014)
Ph.D Students(first position shown):
Postdoctoral Fellows Mentored (current position shown):