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Research

Publications and Preprints

  1. Lagrangian zigzag cobordisms, with Joshua M. Sabloff, David Shea Vela-Vick, and Angela Wu.
    Preprint.
    On the arXiv: arXiv:2308.02057.

  2. Spectral GRID invariants and Lagrangian cobordisms, with Mitchell Jubeir,† Ina Petkova, Noah Schwartz,† and Zachary Winkeler.*
    Preprint.
    On the arXiv: arXiv:2303.16130.

  3. On the tau invariants in monopole and instanton Floer theories, with Sudipta Ghosh and Zhenkun Li.
    Submitted for publication.
    On the arXiv: arXiv:1910.01758.

  4. Upper bounds for the Lagrangian cobordism relation on Legendrian links, with Joshua M. Sabloff and David Shea Vela-Vick.
    Algebr. Geom. Topol., to appear.
    On the arXiv: arXiv:2105.02390.

  5. 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 (pending).

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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

Articles in Preparation

  1. On the naturality of grid homology, with Haofei Fan and Marco Marengon.

  2. Annular link Floer homology and 𝔤𝔩1|1, with Andrew Manion and Ina Petkova.

  3. Cyclic branched covers and combinatorial invariants of transverse knots, with Lucas Meyers,* Robert Quarles,* Brandon Roberts,† and David Shea Vela-Vick.
*: Graduate student at the time of the research
†: Undergraduate student at the time of the research

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:
Sep 11, 2023