Current Research

I am studying the relationship between the ideal of a finite set of points in the projective plane and the ideal of cones over the points. How does the geometric arrangement of the points impact this relationship?

Previous Research

  1. Quandle Coloring Quivers (with Sam Nelson). Journal of Knot Theory and Its Ramifications, Vol. 28, No. 01; https://arxiv.org/abs/1807.10465

  2. Quandle Cocycle Quivers (with Sam Nelson). Topology and its Applications, Vol. 268; https://arxiv.org/abs/1904.09207

  3. Density of Periodic Points of Lattès maps of Finite Fields (with Zoë Bell, Jasmine Camero, Trevor Hyde, Chieh-Mi Lu, Bianca Thompson, Eric Zhu). Journal of Number Theory; https://arxiv.org/abs/2103.00074

  4. Generalizations of Triangle Inequalities to Spherical and Hyperbolic Geometry (with Jacob Naranjo). https://arxiv.org/abs/1805.11442

colored diagram of part of a knot illustrating how crossings correspond to the quandle operation
the nine colorings of a trefoil knot with the colors green, pink, and blue
a snowflake shaped graph

some Inkscape diagrams I made in my previous life as an algebraic knot theorist