Research
Research
My research interests lie in low dimensional topology, especially the interactions of Heegaard Floer homology, Khovanov homology, knot theory and contact geometry.
Here are some of my current/past research projects. Any comments or questions are welcome!
Closures of 3-braids and detection, Pacific Journal of Mathematics
The CFK^infinity type of almost L-space knots, Michigan Mathematical Journal.
(1,1) almost L-space knots, with Hugo Zhou, Indiana University Mathematics Journal.
A Rank Bound In Link Floer Homology and Detection Results, with Subhankar Dey, Quantum Topology.
Cable Links, Annuli and Sutured Floer Homology with Subhankar Dey, Mathematical Research Letters.
On the Nonorientable Four-ball Genus of Torus Knots with Sungkyung Kang, Jonathan Simone and Paula Truöl, Algebraic & Geometric topology.
Knot Floer Homology, Link Floer Homology and Link Detection, with Gage Martin, Algebraic & Geometric topology.
Is the geography of Heegaard Floer homology restricted or is the L-space conjecture false?, with Antonio Alfieri.
Floer homology, clasp-braids and detection results, with Subhankar Dey.
Studying links via book links: a Markov theorem, with Román Aranda and Margaret Doig.
Degree-1 maps and rank inequalities in Heegaard Floer homology, with Sudipta Ghosh.
Diana Hubbard and I are writing a paper on fractional Dehn twist coefficients and categorified knot invariants.
Shunyu Wan and I are working on a project on the geography question for knot Floer homology.
Subhankar Dey, Claudius Zibrowius, and I are working on some detection results for four ended tangles.
My thesis is available here. It contains some original results which I may or may not one day incorporate into a paper.
I was a member of the AIM SQuaRE, "3- and 4-dimensional perspectives on untwisting", with Samantha Allen, Hongtaek Jung, Seungwon Kim, and Hannah Turner.