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
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.
Submitted
Hugo Zhou and I have submitted a paper titled (1,1) almost L-space knots.
Sungkyung Kang, Jonathan Simone, Paula Truöl and I have submitted a paper titled On the Nonorientable Four-ball Genus of Torus Knots.
Posted
Antonio Alfieri and I have written a paper titled Is the geography of Heegaard Floer homology restricted or the L-space conjecture false?.
In Progress
Subhankar Dey and I are working on a project concerning links which are nearly braided from the point of view of link Floer homology.
Román Aranda, Magaret Doig and I are doing some work on open book foliations.
Thesis
My thesis is available here. It contains some original results which I may or may not one day incorporate into a paper.