I am interested in complex dynamical systems and computational geometry. My PhD work is on the harmonic caps and convex bodies of planar domains. The figure above shows the Cauliflower Julia set and its associated harmonic cap. Here is my PhD thesis.

Harmonic Caps and Planar Conformal Geometry

In 2021, I mentored two students through the Undergraduate Research Assistant Program (URAP) supported by the Office of Undergraduate Research. The project is titled Polyhedron Development and Polygon Folding, and investigates the relation between planar shapes and the possibly of folding them up into the boundary surfaces of polyhedrons. Our research was featured in The 2021 Virtual Undergraduate Research and Arts Exposition. Part of the project turned into a paper, which is currently under review for publication.

Closed Cap Condition under the Cap Construction Algorithm (arXiv:2210.00198),