I work in the area of algebraic combinatorics, where mathematicians study how counting problems appear in algebra and geometry. In this area, my work intertwines the subfields of combinatorial representation theory, Schubert calculus, and quasisymmetric function theory. Friendly expositions of these fields can be found here, here, and here.
I also enjoy mentoring student projects in this area and further afield. Read more in my (slightly out-of-date) research statement and research mentorship plan.
If you'd like to know more about any of these projects, send me an email and I can tell you about them or send a draft.
With L. Colmenarejo and A. Ram. A box-by-box formula for Koornwinder polynomials.
With A. Abram. An Edelman–Greene type insertion for excedance classes of the symmetric group.
Solo author, Lusztig varieties over matrix Schubert varieties.
With N. Bergeron, P. Nadeau, H. Spink, and V. Tewari. The Quasisymmetric flag variety: a toric complex on noncrossing partitions. arXiv
With N. Andrews, F. Gelinas, E. Schlums, and M. Zabrocki. When are Hopf algebras determined by integer sequences? arXiv.
With N. Bergeron, P. Nadeau, H. Spink, and V. Tewari. Equivariant quasisymmetry and noncrossing partitions. arXiv
With N. Bergeron: The excedance quotient of the Bruhat order, Quasisymmetric Varieties and Temperley-Lieb algebras, To appear in: Journal of the London Math Society (2024). Jounal version; arXiv:2302.10814.
A unipotent realization of the chromatic quasisymmetric function. Algebra and Number Theory (2024). Journal version; arXiv.
A GL-compatible Hopf algebra of unitriangular class functions. Journal of Algebra (2023). Journal version; arXiv:2211.06981.
The combinatorics of normal subgroups in the unipotent upper triangular group, Combinatorial Theory 1 (2021), Paper No. 15. Journal version; arXiv:2012.00108.
FPSAC 2024 extended abstract (with N. Bergeron): Excedance quotients, Quasisymmetric Varieties, and Temperley–Lieb algebras. Séminaire Lotharingien de Combinatoire, 91B (2024), Paper No. 67. Journal Version.
FPSAC 2023 extended abstract: A unipotent realization of the chromatic quasisymmetric function. Séminaire Lotharingien de Combinatoire, 89B (2023), Paper No. 72. Journal Version.