Research

I currently research low-dimensional topology. Exciting results to come!

As an undergrad I researched combinatorics and number theory in the following projects:

In 2023 I attended the Duluth REU, led by Joe Gallian and Colin Defant. My project involved improving some bounds on the expected running times of the Ungarian Markov Chains of certain lattices (see Defant and Li's original paper on Ungarian Markov Chains here). Most notably I proved that the Ungarian Markov Chain on S_n runs in expectation in linear time, and the Ungarian Markov Chain on the nth Tamari lattice takes at least n^{1-o(1)} moves in expectation. Probably the most interesting aspect of this paper is the proof of the Tamari lattice bound, where I used several "self-similarity" properties of Tam_n to inductively bootstrap an n^{1-o(1)} bound.
In 2022 I attended the UVa REU, led by Ken Ono. There I worked with Quanlin Chen (under the mentorship of Jesse Thorner) to produce some unconditional error bounds on the Sato-Tate distributions for a few special families of surfaces closely related to elliptic curves.