My current interests lie in algebraic combinatorics, enumerative combinatorics and representation stability. I particularly enjoy using representation theory to better understand generally unruly objects in commutative algebra via combinatorics. Recently, I have been most interested in how different types of pattern avoidance interact with other properties of permutations.

For students: If you're interested in getting a sense for what research in math looks like, please reach out. There are many problems in enumerative combinatorics that are accessible and fun! If you're at the Naval Academy, SM291 and SM239 should be more than enough background.

Research

Characterizing avoidance in cycles via vincular patterns

Submitted arXiv (last updated 5/15/2025)

Binary operations on pattern-avoiding cycles

with Kassie Archer and Christina Graves Submitted arXiv (last updated 5/8/2025)

Pattern avoidance in non-crossing and non-nesting permutations

with Kassie Archer Submitted arXiv (last updated 2/19/2025)

Pattern-avoiding shallow permutations

with Kassie Archer and Aaron Geary Submitted arXiv (last updated 12/17/2024)

Pattern avoidance and the fundamental bijection

with Kassie Archer Submitted arXiv (last updated 07/08/2024)

Pattern restricted permutations of small order

with Kassie Archer Discrete Math., to appear arXiv (last updated 02/24/2024)

Systems of ideals parametrized by combinatorial structures

with Andrew Snowden Submitted arXiv (last updated 04/07/2023)

An antichain of monomial ideals in a twisted commutative algebra

Proc. Amer. Math. Soc. 152 (2024), no. 6, 2297-2316 arXiv (last updated 07/16/2021)

Syzygies of P^1 x P^1: data and conjectures

with Juliette Bruce, Daniel Corey, Daniel Erman, Steve Goldstein, Jay Yang J. of Alg. 593 (2022), 598-621 arXiv (last updated 10/05/2019)

Equivariant prime ideals for infinite dimensional supergroups

with Andrew Snowden Trans. Amer. Math. Soc. 377 (2024), 8605-8632 arXiv (last updated 10/05/2019)

Representation stability for sequences of 0-Hecke modules

Alg. Comb. 4 (2021), no. 4, 619-661 arXiv (last updated 10/05/2019)

Computing Schur complexes

with Michael K. Brown, Hang Huang, Michael Perlman, Claudiu Raicu, Steven V Sam, Joao Pedro Santos J. Softw. Alg. Geom. 9 (2019) 111-119 arXiv (last updated 11/18/2019)

The spin-Brauer diagram algebra

J. Algebraic Comb. 50 (2019) 191–224 arXiv (last updated 11/6/2018)

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