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Research

Articles and Preprints

  1. Using knot Floer invariants to detect prime knots, with Samantha Allen, Charles Livingston, and Misha Temkin.
    Submitted for publication.
    On the arXiv: arXiv:2311.11089.

  2. Lagrangian zigzag cobordisms, with Joshua M. Sabloff, David Shea Vela-Vick, and Angela Wu.
    Submitted for publication.
    On the arXiv: arXiv:2308.02057.

  3. Spectral GRID invariants and Lagrangian cobordisms, with Mitchell Jubeir,† Ina Petkova, Noah Schwartz,† and Zachary Winkeler.*
    Studia Sci. Math. Hungar. 61 (2024), no. 4, 311–340.
    On the arXiv: arXiv:2303.16130.
    Review on MathSciNet (pending).

  4. Upper bounds for the Lagrangian cobordism relation on Legendrian links, with Joshua M. Sabloff and David Shea Vela-Vick.
    Algebr. Geom. Topol. 24 (2024), no. 8, 4237–4263.
    On the arXiv: arXiv:2105.02390.
    Review on MathSciNet (pending).

  5. On the tau invariants in monopole and instanton Floer theories, with Sudipta Ghosh and Zhenkun Li.
    J. Topol. 17 (2024), no. 2, e12346, 53 pages.
    On the arXiv: arXiv:1910.01758.
    Review on MathSciNet (pending).

  6. Ribbon homology cobordisms, with Aliakbar Daemi, Tye Lidman, and David Shea Vela-Vick.
    Adv. Math. 408 (2022), 108580, 68 pages.
    On the arXiv: arXiv:1904.09721.
    Review on MathSciNet.

  7. An unoriented skein relation via bordered–sutured Floer homology, with David Shea Vela-Vick.
    J. Symplectic Geom. 19 (2021), no. 6, 1495–1561.
    On the arXiv: arXiv:1811.00134.
    Review on MathSciNet.

  8. Lagrangian cobordisms and the Legendrian invariants in knot Floer homology, with John A. Baldwin and Tye Lidman.
    Michigan Math. J. 71 (2022) no. 1, 145–175.
    On the arXiv: arXiv:1907.09654.
    Review on MathSciNet.

  9. Skein relations for tangle Floer homology, with Ina Petkova.
    Quantum Topol. 11 (2020), no. 1, 119–225.
    On the arXiv: arXiv:1611.04065.
    Review on MathSciNet.

  10. Grid diagrams and Manolescu's unoriented skein exact triangle for knot Floer homology.
    Algebr. Geom. Topol. 17 (2017), no. 3, 1283–1321.
    On the arXiv: arXiv:1305.2562.
    Review on MathSciNet.

  11. From self-similar structures to self-similar groups, with Daniel J. Kelleher and Benjamin A. Steinhurst.
    Internat. J. Algebra Comput. 22 (2012), no. 7, 1250056, 16 pages.
    On the arXiv: arXiv:1011.1817
    Review on MathSciNet.
*: Graduate student at the time of the research
†: Undergraduate student at the time of the research

Other Publications

  1. Lecture notes on Heegaard Floer homology, with Sarah Zampa.
    Singularities and Low Dimensional Topology, Bolyai Soc. Math. Stud., vol. 30, Springer Cham, 2024.
    These are the notes for a lecture series on Heegaard Floer homology that I gave at the Winter School at the Rényi Institute in January 2023, as part of a special semester titled Singularities and Low Dimensional Topology. Based on notes taken by Sarah Zampa.
    On the arXiv: arXiv:2402.07558.
    Videos of the lectures: Lecture 1; Lecture 2; Lecture 3; Lecture 4.

Software

  1. KnotFinder, based on a previous version by Jae Choon Cha, and powered by binaries found in Knotscape, an interactive program written by Jim Hoste and Morwen Thistlethwaite.
    From the DT notation of a knot diagram, KnotFinder attempts to identify each connected summand of the represented knot. Improvements from the previous version include the new abilities to recognize the unknot, prime knots of crossing number 14 to 16, and composite knots. KnotFinder is hosted on KnotInfo, a knot database maintained by Chuck Livingston and Allison Moore.

  2. transverse-hfk-revision, with Lucas Meyers,* Robert Quarles,* Brandon Roberts,† and David Shea Vela-Vick.
    A revision of the program TransverseHFK.c, written by Lenhard Ng, Peter Ozsváth, and Dylan Thurston, with minor bug fixes and improvements in computational efficiency. Also computes invariants in cyclic branched covers.
*: Graduate student
†: Undergraduate student

Slides from Previous Talks

  1. Ribbon homology cobordisms.
    CMS 2019 Winter Meeting, Chelsea Hotel, Toronto, ON.

  2. Upper bounds for the Lagrangian cobordism relation on Legendrian links.
    Nearly Carbon Neutral Geometric Topology Conference 2021, online.

  3. GRID invariants obstruct decomposable Lagrangian cobordisms.
    AMS Spring 2019 Southeastern Sectional Meeting, Auburn University, Auburn, AL.

  4. An unoriented skein exact triangle for tangle Floer homology.
    AMS Spring 2017 Eastern Sectional Meeting, Hunter College, CUNY, New York, NY.

  5. From self-similar structures to self-similar groups.
    AMS Fall 2010 Eastern Sectional Meeting, Syracuse University, Syracuse, NY.

Support

My research has been supported by NSERC Discovery Grant RGPIN-2023-05123, NSF Standard Grant DMS-2238131 (previously DMS-2039688), and an AMS–Simons Travel Grant. The support specific to each paper is listed in the paper itself.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSERC, the NSF, or the AMS.

Page last updated:
Feb 13, 2025