I graduated in 2017 from the University of Washington, Seattle, with a B.S. in mathematics and a minor in music.

Starting September 2023, I will be a lecturer in the Department of Mathematics and Computer Science at Santa Clara University.

Office: East Hall 2860

I've also looked at Brascamp-Lieb inequalities, integral inequalities associated to certain quiver representations, with Harm Derksen.

Overall, I enjoy any math that involves pictures with arrows in them.

- With David Speyer and Hugh Thomas: "Shard modules." Preprint, arXiv:2303.16332, 2023.

There's a close connection between preprojective algebras associated to Dynkin diagrams and the convex geometry of Coxeter groups (as detailed in this paper of Hugh's). Specifically, brick modules of the preprojective algebra biject with shards of the Coxeter group. This paper proves a similar result for preprojective algebras of non-Dynkin diagrams, though we have to impose a couple additional conditions on bricks. My main contributions to this paper were showing that the extra conditions we impose on bricks actually are necessary (by using a computer search to find a brick which satisfied one but not the other) and fixing up the technical details of the framework we use for dealing with non-simply-laced diagrams.

- "Stability of stretched root systems, root posets, and shards." The Electronic Journal of Combinatorics, 28(3), 2021.

One thing that almost all infinite families of finite and affine Coxeter groups have in common is that their Coxeter diagrams are obtained by inserting a long path into a fixed diagram. This paper looks at this "insert a long path" construction for any diagram, and shows how some related constructions (the root poset and the arrangement of shards) stabilize. The original inspiration for this came from wanting a nice uniform description of the bricks of type D preprojective algebras, though this paper is purely combinatorial.

- With David Jekel, Avi Levy, Austin Stromme, and Collin Litterell: "Algebraic Properties of Generalized Graph Laplacians: Resistor Networks, Critical Groups, and Homological Algebra." SIAM J. Discrete Math., 32(2), 1040--1110, 2018. Preprint: arXiv:1604.07075.

This came out of the 2015 REU at the University of Washington. The basic idea is to build up a general foundation for talking about the sandpile group or critical group of a graph, allowing for coefficient rings other than

**Z**, and to connect this to a bunch of other things. I wasn't directly involved with much of this paper, but I computed a lot of examples and worked on the material that became section 7. - "Seeing Galois Theory on Riemann Surfaces with Dessins d'Enfants." 2017.

My senior thesis, an exposition on dessins d'enfants. Written under the guidance of Professor Jim Morrow. The plan was to explain the arguments in Ernesto Girondo and Gabino GonzĂˇlez-Diez's Introduction to Compact Riemann Surfaces and Dessins d'Enfants in a way I could understand better.

- With David Jekel: A note on critical groups of graphs with dihedral symmetry.

The number of spanning trees of an undirected Cayley graph of the cyclic group of order n is always n times a perfect square. This note arose out of trying to find a nice algebraic explanation of this fact using sandpile groups.

- See also "Teaching - Mathcamp" below.

Winter 2018: Math 115.

Fall 2018: Math 116.

Winter 2019: Math 116.

Fall 2021: Math 105.

(the latter third of) Winter 2022: Math 115.

Summer 2022: M-STEM Level 2 Math.

Winter 2023: I was the Graduate Student Mentor (GSM), doing odd jobs helping out the introductory classes (and substituting a lot).

Here are notes for my class on quiver representations.

Here are notes for my class on determinants.

Here is a note on why the groundskeeper's algorithm for generating uniformly random spanning trees works.

Here are notes on my one-day class on matroids.

I also visited for a week in summer 2022 and taught a two-day class on combinatorial reciprocity.

Please let me know if you find typos.

In summer 2021, I ran a grad student minicourse on Ringel-Hall algebras, following Kirillov's

In summer 2022, I organized the grad student minicourses. See this page for details.

In summer 2023, I'm organizing the grad student minicourses. See this page for details.

- Outside of math, I enjoy puzzles and games, music (in particular electronic music -- here is some that I made), comics, and long walks.
- For non-math content, see my personal webpage.
- I was interviewed for this article about the Putnam exam at UW.