Research

Current research

My research interests are knot theory, categorification, representation theory, and low-dimensional topology.

I do not have any papers yet in my areas of interest, but I am working on a project about constructing the generating functions for colored HOMFLY-PT "polynomials" of rational tangles and links from the geometry of 2-bridge diagrams. Stay tuned for the paper! After this, I plan to apply these results to study the colored HOMFLY-PT homology of these objects.

Here is an ever-growing list of mathematical topics I want to think about someday (in no particular order):

Non type-A link homology
The AJ Conjecture
The Volume Conjecture
Skein lasagna modules
Incompressible surfaces in knot exteriors
Graph homology
Annular Khovanov homology
Knotted surfaces
(Quantum) cluster algebras

Undergraduate research

My previous research was in graph theory, where I studied algebraic and combinatorial properties of prime graphs as part of an REU with Texas State University. I also participated in a project for my undergraduate complex analysis course, which led to a couple of publications.

Here is a list of my undergrad publications:

1. Minimal Prime Graphs of Finite Solvable Groups, Chris Florez, Jonathan Higgins, Kyle

Huang, Thomas M. Keller, Dawei Shen, preprint, accepted pending revisions by Rocky

Mountain Journal of Mathematics, arXiv:2011.10403 [math.CO]

2. The Adjacency Spectra of Some Families of Minimally Connected Prime Graphs, Chris

Florez, Jonathan Higgins, Kyle Huang, Thomas M. Keller, Dawei Shen, Involve, Vol. 17

(2024), No. 1, 107–120, arXiv:2011.08938 [math.CO]

3. **The Prime Graphs of Some Classes of Finite Groups, Chris Florez, Jonathan Higgins, Kyle Huang, Thomas M. Keller, Dawei Shen, Yong Yang, Journal of Pure and Applied Algebra, 226 (2022), 106990, 19 pp., arXiv:2101.00363 [math.GR]

4. A Groundwater Contaminant Extraction Model Using Complex Potentials, Paul Isihara, Lucy Henneker, Andrew Luhmann, Nathaniel Bowden, Daws Bremner, Jonathan Higgins,

Stephen McKay, Julio Reyes, UMAP Journal 43.1, 2022, 39-76

**I am listed as an author of this paper as part of the REU group, but I did not work on this paper in particular.

Page updated

Google Sites

Report abuse