Research

The material below is based on research partially supported by the National Science Foundation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

  1. A topological model for the HOMFLY-PT polynomial, with Cristina Ana-Maria Anghel, submitted. [arXiv] [Talk]
  2. Computing Khovanov homology via categorified Jones-Wenzl projectors, submitted.
  3. Stable Khovanov homology and volume, accepted for publication in the Proceedings of the American Mathematical Society. [arXiv] 
  4. Normal surface theory and colored Khovanov homology. [arXiv]
  5. Jones diameter and crossing number of knots, with Efstratia Kalfagianni, Advances in Mathematics, 417: Paper No. 108937, 35, DOI 10.1016/j.aim.2023.108937, 2023.
  6. Jones slopes and coarse volume of near-alternating links, Communications in Analysis and Geometry, Vol. 30, no. 4, 2022.
  7. Colored Jones polynomials without tails, with Roland van der Veen, Algebraic and Geometric Topology, 22-6, 2857–2865, DOI
    10.2140/agt.2022.22.2857, 2022.
  8. On Khovanov Homology and Related Invariants, with Carmen Caprau, Nicolle Gonzalez, Adam M. Lowrance, Radmila Sazdanovic, and Melissa Zhang, Research Directions in Symplectic and Contact Geometry and Topology. Association for Women in Mathematics Series, vol 27. Springer, Cham, DOI 10.1007/978-3-030-80979-9_6, 2021.
  9. Cancellations in the degree of the colored Jones polynomial, with Roland van der Veen, Acta
    Mathematica Vietnamica, Proceedings of Quantum Topology and Hyperbolic Geometry in Da Nang,     DOI 10.1007/s40306-021-00423-4, 2021.
  10. On 3-braids and L-space knots, with Faramarz Vafaee, Geometriae Dedicata, DOI
    10.1007/s10711-020-00594-8, 2021
  11. Stability and Triviality of the Transverse Invariant from Khovanov Homology, with Diana
    Hubbard, Topology and Its Applications, DOI:10.1016/j.topol.2020.107146, 2020.
  12. The Slope Conjecture for Montesinos knots, with Stavros Garoufalidis and Roland van der
    Veen, International Journal of Mathematics, DOI: 10.1142/S0129167X20500561, 2020.
  13. Stability properties of the colored Jones polynomial, Journal of Knot Theory and its
    Ramifications,     28, No. 08, 2019.
  14. Normal and Jones surfaces of knots , with Efstratia Kalfagianni, Journal of Knot Theory and
    its Ramifications     , 27, Issue 6, 2018.
  15. A trivial tail homology for non A-adequate links, Algebraic and Geometric Topology, 18, no.
    3, p. 1481–1513, 2018.
  16. Slopes for pretzel knots, with Roland van der Veen, New York Journal of Mathematics, 22,
    p. 1339–1364, 2016.
  17. Crosscap numbers and the Jones polynomial, with Efstratia Kalfagianni, Advances in
    Mathematics     , 286, p. 308-337, 2016.
  18. On the degree of the colored Jones polynomial, with Efstratia Kalfagianni, Acta Mathematica
    Vietnamica,     Proceedings of Quantum Topology and Hyperbolic Geometry in Nha Trang, May
    2013, 39(4), 2014.