Research

Research Interests

Publications/Preprints

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

*undergraduate student