Research
Research
HOMFLYPT homology for oriented tangles, joint with William Ballinger. In preparation.
Doubly-graded exponential growth of colored torus knot homology. 2025, Under review.
Fray functors and equivalence of colored HOMFLYPT homologies. Quantum Topology (2025), published online first.
Row-Column mirror symmetry for colored torus knot homology. Selecta Mathematica, 30 (2024), no. 97.
The papers above give an algorithm for computing the column-colored HOMFLY homology of positive torus knots in various models. Here is a program which implements this algorithm. If you find this program helpful or want to report bugs or suggest improvements, please email me!
I gave a minicourse on "Categorified Projectors and Colored HOMFLY Homology" in Belalp, Switzerland from September 1-4, 2025. You can find the notes from this course here.