I am a fourth-year graduate student in the University of Washington's math department, studying algebraic combinatorics. My advisor is Ricky Liu.

I was an undergraduate at MIT, class of 2021, obtaining a bachelor's degree in mathematics with a minor in computer science.

I participate in the MIT Mystery Hunt, as well as many other puzzlehunts, on team NES. I also helped develop Noq, a website housing a suite of solvers for many genres of Nikoli-style logic puzzles.

Publications

• (November 2024) Generalized degree polynomials of trees (with Ricky Liu). Available at https://arxiv.org/abs/2411.18972.
  The generalized degree polynomial $\mathbf{G}_T(x,y,z)$ of a tree $T$ is an invariant introduced by Crew that enumerates subsets of vertices by size and number of internal and boundary edges. Aliste-Prieto et al. proved that $\mathbf{G}_T$ is determined linearly by the chromatic symmetric function $\mathbf{X}_T$, introduced by Stanley. We present several classes of information about $T$ that can be recovered from $\mathbf{G}_T$ and hence also from $\mathbf{X}_T$. Examples of such information include the double-degree sequence of $T$, which enumerates edges of $T$ by the pair of degrees of their endpoints, and the leaf adjacency sequence of $T$, which enumerates vertices of $T$ by degree and number of adjacent leaves. We also discuss a further generalization of $\mathbf{G}_T$ that enumerates tuples of vertex sets and show that this is also determined by $\mathbf{X}_T$.
  
  
• (October 2023) Shuffle bases and quasisymmetric power sums (with Ricky Liu). Available at https://arxiv.org/abs/2310.09371.
  We characterize isomorphisms between the algebra $\text{QSym}$ of quasisymmetric functions and the shuffle algebra $\text{Sh}$ of compositions. To do so, we establish a universal property for $\text{Sh}$ analogous to the one for $\text{QSym}$ described by Aguiar, Bergeron, and Sottile. We then use these results to derive characterizations of quasisymmetric power sums and study some particular examples from the literature.