Research

My research interests are in low dimensional topology, knot theory, and graph theory. Students interested in a research project under my supervision should email me.

Papers and preprints. (Undergraduate coauthors marked with *)

  1. Average signature and 4-genus of 2-bridge knots. Joint with Moshe Cohen, Neal Madras, and Steven Raanes*. arXiv:2406.17738.
  2. The distribution of braid indices of 2-bridge knots. Joint with Tobias Clark* and Jeremy Frank*. To appear in  J. Knot Theory Ramifications. arXiv:2401.08388.
  3. The distribution of genera of 2-bridge knots. Joint with Moshe Cohen, Abigail Dinardo*, Steven Raanes*, Izabella M. Rivera*, Andrew J. Steindl*, and Ella S. Wanebo*. To appear in  Fund. Math. arXiv:2307.09399.
  4. Near extremal Khovanov homology of Turaev genus one links. Joint with Theo Beldin*, Mia DeStefano*, Wyatt Milgrim*, and Cecilia Villaseñor*. Topology Appl. 346 (2024), 108861. arXiv:2211.100009.
  5. The average genus of a 2-bridge knot is asymptotically linear. Joint with Moshe Cohen. New York J. Math. 30 (2024), 1032-1055. arXiv:2205.06122.
  6. On Khovanov homology and related invariants. Joint with Carmen Caprau, Nicolle González,  Christine Ruey Shan Lee, Radmila Sazdanović, and Melissa Zhang. Research Directions in Symplectic and Contact Geometry and Topology, Springer, 2021.  arXiv:2002.05247.
  7. The multi-region index of a knot. Joint with Sarah Goodhill*, Valeria Munoz Gonzales*, Jessica Rattray*, and Amelia Zeh*.  J. Knot Theory Ramifications. 29 (2020), no. 4, 16pp. arXiv:1909.11831.
  8. Torsion in thin regions of Khovanov homology. Joint with Alex Chandler, Radmila Sazdanović, and Victor Summers. Canadian Journal of Mathematics. 74. (2022), no. 3, 630-654. arXiv:1903.05760.
  9. Extremal Khovanov homology of Turaev genus one links. Joint with Oliver Dasbach. Fund. Math. 250 (2020), 63-99. arXiv:1812.11387.
  10. The 2-factor polynomial detects even perfect matchings. Joint with Scott Baldridge and Ben McCarty. Electron. J. Combin. 27 (2020), no. 2, Paper No. 2.27, 16 pp. arXiv:1812.10346.
  11. Alternating distances of knots. Encyclopedia of Knot Theory. CRC Press, 2021.
  12. The Jones polynomial of an almost alternating link. Joint with Dean Spyropoulos*. New York J. Math. 23 (2017), 1611-1639. arXiv:1707.05443.
  13. The Turaev genus of torus knots. Joint with Kaitian Jin*, Eli Polston*, and Yanjie Zheng*.  J. Knot Theory Ramifications. 26 (2017), no. 14, 1750095, 28 pp. arXiv:1703.02506.
  14. Chromatic homology, Khovanov homology, and torsion. Joint with Radmila Sazdanović. Topology Appl. 222 (2017), 77-99. arXiv:1609.03585.
  15. Invariants for Turaev genus one links. Joint with Oliver Dasbach. Comm. Anal. Geom. 25 (2018), no. 5, 1103-1126. arXiv:1604.03501.
  16. Turaev genus and alternating decompositions. Joint with Cody Armond. Algebr. Geom. Topol. 17 (2017), 793-830. arXiv:1507.02771.
  17. Alternating distances of knots and links. Topology Appl. 182 (2015), 53-70. arXiv:1406.7039.
  18. A Turaev surface approach to Khovanov homology. Joint with Oliver Dasbach. Quantum Topol. 5 (2014), no. 4, 425-486. arXiv:1107.2344.
  19. Turaev genus, knot signature, and the knot homology concordance invariants. Joint with Oliver Dasbach. Proc. Amer. Math. Soc. 139 (2011), no. 7, 2631-2645. arXiv:1002.0898.
  20. The Khovanov width of twisted links and closed 3-braids. Comment. Math. Helv. 86 (2011), no. 3, 675-706. arXiv:0901.2196.
  21. Cube diagrams and 3-dimensional Reidemeister-like moves for knots. Joint with Scott Baldridge. J. Knot Theory Ramifications 21 (2012), no. 5, 125033, 39 pp. arXiv:0811.0225.
  22. On knot Floer width and Turaev genus. Algebr. Geom. Topol. 8 (2008), no. 2, 1141-1162. arXiv:0709.0720.