Research

I study symmetric functions and their connections to geometry and representation theory. Symmetric functions are functions invariant under permutations of their variables and form a ring with several notable bases, most prominently the Schur functions. Schur functions are defined as sums over semistandard Young tableaux and play a key role in algebraic geometry and representation theory. We say that a symmetric function is Schur positive if it expands as a nonnegative sum of Schur functions, a property that often reflects deep algebraic or geometric structure.

For any symmetric function, there are two natural problems I study: (1) identify the combinatorial objects that generate it, and (2) determine its Schur positivity. 

Publications

1. Uncrowding the 5-Vertex Model: RSK and Crystal Structures

with Lisa Johnston and Anne Schilling. Submitted. arXiv: 2606.02972

2. The Immersion Poset on Partitions

with Lisa Johnston, David Kenepp, Digjoy Paul, Anne Schilling, Mary Claire Simone, and Regina Zhou. Journal of Algebraic Combinatorics Vol 61, (2025). arXiv: 2404.07393 

3.  The kernel of newform Dedekind sums

with Juan J. Ramirez and Matthew P. Young. Journal of Number Theory Vol 223, pp. 53-63 (2021).   

Undergraduate:

• In 2020, I participated in a virtual REU hosted by Texas A&M. I was a member of the Number Theory group mentored by Matthew P. Young. We expanded on work from previous REU students and examined the kernel of newform Dedekind sums which are a class of homomorphisms arising from newform Eisenstein series. Our work resulted in a publication in the Journal of Number Theory.

• For my undergraduate thesis, I developed Sage code to compute invariant polynomials of coregular representations of SL(n) which are representations admitting a Hilbert basis with no relations.