Research

Interests

Broadly speaking, my mathematical interest is in complex dynamical systems and computational geometry. I think about geometric folding problems that arise from dynamics on the complex plane. To be more specific, I study how planar shapes and their corresponding harmonic caps glues and folds into the boundary surface of a convex region in space. My favorite example is the Cauliflower Julia set and its associated harmonic cap.

Projects

Polyhedron development and polygon folding

The baby steps of studying harmonic caps are to study cap constructions of polygons. For example, a square can be viewed as an octagon with a corresponding cap glued along the boundary. The construction results in the boundary surface of a square antiprism.

Together with Mercedes Sandu (NU'24) and Jade Zhang (NU'24), we classified the polygons that are possible for such cap construction. The project was featured in The 2021 Virtual Undergraduate Research and Arts Exposition. Part of the project turned into a paper, which has been accepted for publication in Involve, a Journal of Mathematics.

Research writings

Preprints

Harmonically planar Jordan domains and arcs.
Preprint, 18 pages, September 2022.

Publications

Closed cap condition under the cap construction algorithm, with M. Sandu and J. Zhang
To appear, Involve, a Journal of Mathematics, 13 pages, arXiv:2210.00198.
A convenient direct laser writing system for the creation of microfluidic masters, with C. LaFratta, O. Simoska, I. Pelse, and M. Ingram.
Microfluid Nanofluid, 19 (2015), 419–426, doi:10.1007/s10404-015-1574-4.

Theses

Harmonic caps and planar conformal geometry.
PhD thesis, Northwestern University, 2020. PDF
Homeomorphism groups of fractals.
Senior project, Bard College, 2015. PDF
Using a radical scavenger and modeling the improvement of linewidth in one-photon direct laser writing lithography.
Senior project, Bard College, 2014. PDF

Coding

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