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!
Accepted Papers
Knot Floer Homology, Link Floer Homology and Link Detection, with Gage Martin, Algebraic & Geometric topology.
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, Paula Truöl, Algebraic & Geometric topology.
Submitted Papers
Hugo Zhou and I have submitted a paper titled (1,1) almost L-space knots.
Antonio Alfieri and I have written a paper titled Is the geography of Heegaard Floer homology restricted or is the L-space conjecture false?
Subhankar Dey and I have written a paper titled Floer homology, clasp-braids and detection results.
Some other work in progress
Román Aranda, Margaret Doig and I are doing some work on open book foliations.
I am writing a paper with provisional title "3-braids, unknots, and detection results".
Thesis
My thesis is available here. It contains some original results which I may or may not one day incorporate into a paper.
Other Activities
I recently joined an AIM SQuaRE, "3- and 4-dimensional perspectives on untwisting", with Samantha Allen, Seungwon Kim, and Hannah Turner.