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!

Published or Accepted Papers

1. On Heegaard Floer minimal knots in sutured manifolds, Transactions of the American Mathematical Society.

2. Studying links via book links: a Markov theorem, with Román Aranda and Margaret Doig, Canadian Mathematical Bulletin.

3. Closures of 3-braids and detection, Pacific Journal of Mathematics.

4. The CFK^infinity type of almost L-space knots, Michigan Mathematical Journal.

5. (1,1) almost L-space knots, with Hugo Zhou, Indiana University Mathematics Journal.

6. A Rank Bound In Link Floer Homology and Detection Results, with Subhankar Dey, Quantum Topology.

7. Cable Links, Annuli and Sutured Floer Homology with Subhankar Dey, Mathematical Research Letters.

8. On the Nonorientable Four-ball Genus of Torus Knots with Sungkyung Kang, Jonathan Simone and Paula Truöl, Algebraic & Geometric topology.

9. Knot Floer Homology, Link Floer Homology and Link Detection, with Gage Martin, Algebraic & Geometric topology.

Posted/Submitted Papers

1. Fractional Dehn twist coefficients and rank bounds for categorified link invariants, with Diana Hubbard 

2. The next-to-top term of the knot Floer homology of some non-fibered knots, with Shunyu Wan.

3. Real sutured Heegaard Floer homology, with Gary Guth, and Yonghan Xiao.

4. Is the geography of Heegaard Floer homology restricted or is the L-space conjecture false?, with Antonio Alfieri.

5. Floer homology, clasp-braids and detection results, with Subhankar Dey.

6. Degree-1 maps and rank inequalities in Heegaard Floer homology, with Sudipta Ghosh.

Some Papers In Preparation

1. Subhankar Dey, Claudius Zibrowius, and I are working on two papers on detection results for Conway tangles.

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 was a member of the AIM SQuaRE, "3- and 4-dimensional perspectives on untwisting", with Samantha Allen, Hongtaek Jung, Seungwon Kim, and Hannah Turner.