Publications and Preprints
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Upper bounds for the Lagrangian cobordism relation on Legendrian links, with Joshua M. Sabloff and David Shea Vela-Vick.
Submitted for publication.
On the arXiv: arXiv:2105.02390. -
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. -
Ribbon homology cobordisms, with Aliakbar Daemi, Tye Lidman, and David Shea Vela-Vick.
Adv. Math., accepted for publication.
On the arXiv: arXiv:1904.09721. -
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. -
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 (pending). -
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. -
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. -
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.
Articles in Preparation
- On the naturality of grid homology, with Haofei Fan and Marco Marengon.
- Annular link Floer homology and 𝔤𝔩1|1, with Andrew Manion and Ina Petkova.
- Cyclic branched covers and combinatorial invariants of transverse knots, with Lucas Meyers,* Robert Quarles,* Brandon Roberts,† and David Shea Vela-Vick.
†: Undergraduate student
Software
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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. -
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.
†: Undergraduate student
Slides from Previous Talks
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Upper bounds for the Lagrangian cobordism relation on Legendrian links.
Nearly Carbon Neutral Geometric Topology Conference 2021, online. -
Ribbon homology cobordisms.
Tech Topology Conference 2019, Georgia Institute of Technology, Atlanta, GA. -
GRID invariants obstruct decomposable Lagrangian cobordisms.
AMS Spring 2019 Southeastern Sectional Meeting, Auburn University, Auburn, AL. -
An unoriented skein exact triangle for tangle Floer homology.
AMS Spring 2017 Eastern Sectional Meeting, Hunter College, CUNY, New York, NY. -
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 NSF Standard Grant 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 National Science Foundation.