My research lies at the interface of computational/homological algebra, algebraic combinatorics, representation theory, and algebraic geometry. I utilize tools from topological, tropical, and algebraic combinatorics to investigate homological aspects of algebras with a group action and/or combinatorial structure.
14. Ribbon complexes for the 0-Hecke algebra (with Bryan Lu).
We construct explicit tableau-level maps between indecomposable projective modules for the type A 0-Hecke algebra that assemble into canonical split short exact sequences lifting the basic ribbon product rule in NSym via concatenation and near-concatenation. Iterating these maps yields cochain complexes indexed by generalized ribbons; we prove these complexes are acyclic in positive degrees and that their zeroth cohomology is the projective module indexed by full concatenation. We apply these complexes, together with VandeBogert's ribbon Schur module criterion, to prove Koszulness for a naturally defined internally graded algebra object built from the 0-Hecke tower. Finally, we define skew projective modules whose noncommutative Frobenius characteristics realize skewing by fundamental quasisymmetric functions on NSym.
13. Standard Monomials for Positroid Varieties (with Shiliang Gao and Daoji Huang). To appear in Advances in Mathematics.
We give an explicit characterization of the standard monomials of positroid varieties with respect to the Hodge degeneration, and give a Grobner basis for positroid varieties. As an application, we show that promotion on rectangular-shaped semistandard tableaux gives a bijection between standard monomials of a positroid variety and its cyclic shifts.
12. Alexander Duals of Symmetric Simplicial Complexes and Stanley-Reisner Ideals (with Katie Bruegge, Martina Juhnke, Uwe Nagel, and Sasha Pevzner). To appear in Advances in Applied Mathematics, Volume 178, July 2026, 103082.
This project was started at the REACT workshop in March 2021.
11. The MatrixSchubert package for Macaulay2 (with Sean Grate, Daoji Huang, Patricia Klein, Adam LaClair, Yuyuan Luo, and Joseph McDonough). Journal for Software in Algebra and Geometry, Vol. 15, No. 1, 2025. [arXiv]
This paper resulted from the 2023 Macaulay2 workshop in Minneapolis (for which I was a co-organizer), where Patricia Klein and I led this project.
10. Koszulity, supersolvability, and Stirling representations (with Vic Reiner and Sheila Sundaram). Annals of Representation Theory, Volume 2 (2025) no. 2.
We cite the following document by Jörgen Backelin: Low degrees in a Groebner basis may force the Koszul property
9. Root Polytopes, Tropical Types, and Toric Edge Ideals (with Anton Dochtermann and Ben Smith). Algebraic Combinatorics, 8.1 (2025): 59-99.
8. GL-equivariant resolutions over Veronese Rings (with Mike Perlman, Sasha Pevzner, Vic Reiner, and Keller VandeBogert), Journal of the London Mathematical Society, Vol. 109 (2024): e12848. https://doi.org/10.1112/jlms.12848
7. Rees Algebras of Closed Determinantal Facet Ideals (with Kuei-Nuan Lin and Whitney Liske), Journal of Pure and Applied Algebra (2024).
6. Polarizations of Powers of Graded Maximal Ideals (with Gunnar Fløystad and Henning Lohne), Journal of Pure and Applied Algebra, Vol 226, Issue 5 (2022)
This paper was developed during my seven-month research visit to the University of Bergen in 2019.
5. Polarizations and Hook Partitions (with Keller VandeBogert), Journal of Pure and Applied Algebra (2022)
4. Linear Strands of Initial Ideals of Determinantal Facet Ideals (with Keller VandeBogert), Communications in Algebra, DOI: 10.1080/00927872.2021.2002885
3. Determinantal Facet Ideals for Smaller Minors (with Keller VandeBogert), Archiv der Mathematik (2022).
2. The Virtual Resolutions Package for Macaulay2 (with Juliette Bruce, Michael Loper, and Mahrud Sayrafi), Journal for Software in Algebra and Geometry, Vol 10 (2020), pp. 51-60. [arXiv]
This paper resulted from my participation in the Macaulay2 workshop at University of Wisconsin-Madison in April 2018.
Counting polynomials over finite fields with given root multiplicities (with Melanie Matchett Wood) Journal of Number Theory, 136C (2014), pp. 394-402.
This paper resulted from my participation in the "Undergraduate Research Scholars" Program at the University of Wisconsin-Madison.