## Research Interests

**Knot Theory**. I am particularly interested in the Jones polynomial, skein modules, character varieties, the A-polynomial, the Alexander polynomial, and left-orderability of groups.

**Knot Theory**. I am particularly interested in the Jones polynomial, skein modules, character varieties, the A-polynomial, the Alexander polynomial, and left-orderability of groups.

- On the volume conjecture for cables of knots (with T. Le) Journal of Knot Theory and Its Ramifications 19 (2010), no. 12, 1673--1691.
- Proof of a stronger version of the AJ conjecture for torus knots Algebraic and Geometric Topology 13 (2013), no. 1, 609--624.
- The universal character ring of some families of one-relator groups Algebraic and Geometric Topology 13 (2013), no. 4, 2317--2333.
- The universal character ring of the (-2,2m+1,2n)-pretzel link International Journal of Mathematics 24 (2013), no. 8, 13 pages.
- On the twisted Alexander polynomial for representations into SL(2,C) Journal of Knot Theory and Its Ramifications 22 (2013), no. 10, 12 pages.
- The Kauffman bracket skein module of two-bridge links (with T. Le) Proceedings of the American Mathematical Society 142 (2014), no. 3, 1045--1056.
- Twisted Alexander polynomials of 2-bridge knots for parabolic representations (with T. Morifuji) Pacific Journal of Mathematics 269 (2014), no. 2, 433--451.
- On the AJ conjecture for cables of the figure eight knot New York Journal of Mathematics 20 (2014) 727--741.
- Twisted Alexander polynomials with the adjoint action for some classes of knots Journal of Knot Theory and Its Ramifications 23 (2014), no. 10, 10 pages.
- On left-orderable fundamental groups and Dehn surgeries on knots Journal of the Mathematical Society of Japan 67 (2015), no. 1, 319--338.
- On the AJ conjecture for cables of twist knots Fundamenta Mathematicae 230 (2015), no. 3, 291--307.
- On left-orderability and cyclic branched coverings Journal of the Mathematical Society of Japan 67 (2015), no. 3, 1169--1178.
- On the AJ conjecture for knots (with T. Le) Indiana University Mathematics Journal 64 (2015), no. 4, 1103--1151.
- Knot cabling and the degree of the colored Jones polynomial (with E. Kalfagianni) New York Journal of Mathematics 21 (2015), 905--941.
- The strong AJ conjecture for cables of torus knots Journal of Knot Theory and Its Ramifications 24 (2015), no. 14, 11 pages.
- Character varieties of double twist links (with K. Petersen) Algebraic and Geometric Topology 15 (2015), no. 6, 3569--3598.
- Character varieties of (-2,2m+1,2n)-pretzel links and twisted Whitehead links Journal of Knot Theory and Its Ramifications 25 (2016), no. 2, 16 pages.
- Nonabelian representations and signatures of double twist knots Journal of Knot Theory and Its Ramifications 25 (2016), no. 3, 9 pages.
- On nonabelian representations of twist knots (with J. Dean*) pdf Involve - A Journal of Mathematics (to appear).
- Reidemeister torsion and Dehn surgery on twist knots Tokyo Journal of Mathematics (to appear).
- Some families of minimal elements for a partial ordering on prime knots (with F. Nagasato) Osaka Journal of Mathematics (to appear).
- On the AJ conjecture for cable knots. arXiv
- Twisted Alexander polynomials of genus one two-bridge knots. arXiv
- Volumes of double twist knot cone-manifolds. arXiv
- Adjoint twisted Alexander polynomials of genus one two-bridge knots. arXiv

^{*undergraduate student}