My research is in algebraic combinatorics and combinatorial algebraic geometry, and I often think about the interplay between moduli spaces, symmetric functions, (affine) flag varieties, and coinvariant rings.

Publications and Preprints:

1. On Macdonald expansions of q-chromatic symmetric functions and the Stanley-Stembridge conjecture

   • Joint with A. Mellit, M. Romero, K. Weigl, and J. Wen

   • arXiv 2025 (submitted)

2. A geometric interpretation of the Delta Conjecture

   • Joint with M. Gillespie and E. Gorsky

   • arXiv 2024 (submitted)

3. Irreducible components of two-column ∆-Springer fibers

   • Joint with J. Connor and K. Purohit

   • arXiv  2024 (submitted)

4. A combinatorial skewing formula for the Rise Delta Theorem

   • Joint with M. Gillespie and E. Gorsky

   • arXiv 2024 (accepted to Combinatorial Theory)

5. Cocharge and skewing formulas for the ∆-Springer modules and the Delta Conjecture,

   • Joint with M. Gillespie

   • IMRN, 14 (2024) 10895–10917

   • arXiv 

6. Springer fibers and the Delta Conjecture at t=0, 

   • Joint with J. Levinson and A. Woo 

   • Adv. Math., 439 (2024) 109491.

   • arXiv

7. ∆-Springer varieties and Hall-Littlewood polynomials, 

   • Forum Math., Sigma (2024), Vol. 12:e19 1–23

   • arXiv 

8. Degenerations and multiplicity-free formulas for products of ψ and ω classes on \overline{M}_{0,n}, 

   • Joint with M. Gillespie and J. Levinson 

   • Math. Z., 304, 56 (2023)

   • arXiv 

9. Lazy tournaments, and multidegrees of a projective embedding of \overline{M}_{0,n}, 

   • Joint with M. Gillespie and J. Levinson (2021).  

   • Comb. Theory 3 (2023), no. 1, Paper No. 3, 26 pp. 

   • arXiv

10. A proof of a conjecture of Monin and Rana on equations defining \overline{M}_{0,n}, 

    • Joint with M. Gillespie and J. Levinson 

    • arXiv (submitted, 2022)

11. Orbit harmonics for the union of two orbits, 2022. 

    • arXiv.

12. Ordered set partitions, Garsia-Procesi modules, and rank varieties, 

    • Trans. Amer. Math. Soc., 374 (2021), 2609-2660.  

    • arXiv

13. Combinatorics and Representation Theory of Rank Varieties, Springer Fibers, and Hyperplane Arrangements 

    • PhD Thesis, University of Washington

14. Existence and hardness of conveyor belts, 

    • Joint with M. Baird, S.C. Billey, E.D. Demaine, M.L. Demaine, D. Eppstein, S. Fekete, G. Gordon, J.S.B. Mitchell, J.P. Swanson. 

    • Electron. J. Combin., 27(4), 2020. arXiv

15. Labeled binary trees, subarrangements of the Catalan arrangements, and Schur positivity, 

    • Joint with I.M. Gessel and V. Tewari. 

    • Adv. Math, 356 (2019) 106814. arXiv

Other works:

• G-edge colored planar rook algebra,

  • Undergraduate honors thesis, received the distinction of high honors

Extended Abstracts:

1. A cocharge formula for the Delta-Springer modules,

   • Joint with M. Gillespie.

   • Seminaire Lotharingien de Combinatoire, Proceedings of FPSAC 2023 (accepted as a poster). Extended abstract

2. Degenerations and multiplicity-free formulas for products of ψ and ω classes on \overline{M}_{0,n}, 

   • Joint with M. Gillespie and J. Levinson. 

   • Seminaire Lotharingien de Combinatoire, Proceedings of FPSAC 2022 (accepted as a talk). Extended abstract

3. Springer fibers and the Delta Conjecture at t=0, 

   • Joint with J. Levinson and A. Woo. 

   • Seminaire Lotharingien de Combinatoire, Proceedings of FPSAC 2021 (accepted as a talk). Extended abstract

4. Ordered set partitions, Tanisaki ideals, and rank varieties, 

   • Seminaire Lotharingien de Combinatoire, Proceedings of FPSAC 2020 (accepted as a talk). Extended abstract

5. Schur positivity and labeled binary trees, 

   • Joint with I.M. Gessel and V. Tewari. 

   • Seminaire Lotharingien de Combinatoire, Proceedings of FPSAC 2017 (accepted as a poster). Extended abstract

Recorded Talks and Slides:

• FPSAC 2022: Tournaments and slide rules for products of psi and omega classes on \overline{M}_{0,n}

• FPSAC 2021: Springer fibers and the Delta Conjecture at t=0

• FPSAC 2020 (Best Student Presentation Award):  Ordered set partitions, Tanisaki ideals, and rank varieties

• UW Combinatorics Seminar (also my PhD defense).

  •  Preseminar: Combinatorics of coinvariant rings

  • Seminar: Ordered set partitions, Garsia-Procesi modules, and rank varieties

• Labeled binary trees, subarrangements of the Catalan arrangements, and Schur positivity  (slides)

Expository talks and notes:

Some fun expository talks I've given on various topics:

• Crush course in spectral sequences (2020)

• Math Day talk on intersection theory and the moduli space of genus 0 stable curves with marked points (2022)