Research
My research is in algebraic combinatorics, with connections to representation theory, algebraic geometry, and mathematical physics. Much of my recent work focuses on Schubert calculus and the combinatorics of integrable systems (particularly, solvable lattice models). A unifying theme is the search for explicit combinatorial rules for invariants involved in the geometry of the flag variety and the representation theory of Lie groups.
Papers Talks Conferences/Seminars Organized Applets
Papers
- A combinatorial rule for GL-multiplicities of A_n-quiver loci (with Ian Cavey and Alexander Yong), 2026.
- The record statistic and forward stability of Schubert products (with Reuven Hodges and Hanzhang Yin), 2026.
- Lattice Models for Double Whittaker Polynomials and Motivic Chern Classes (with Ben Brubaker, Daniel Bump, and Hunter Spink), 2025.
- On the Boson-Fermion Correspondence for Factorial Schur Functions (with Daniel Bump and Travis Scrimshaw), 2025, to appear in Discrete Mathematics.
- Stability of products of double Grothendieck polynomials (with David Wallach), Int. Math. Res. Not. IMRN. (2025)
- When do Schubert polynomial products stabilize? (with David Wallach), 2024, submitted for publication.
- Factorial Fock free fermions (with Daniel Bump and Travis Scrimshaw), 2024, submitted for publication.
- Solving the n-color ice model (as mentor for 2022 Polymath Jr. program), Ann. Comb. (2025).
- Lattice Models, Hamiltonian Operators, and Symmetric Functions, 2021, submitted for publication.
- Frozen Pipes: Lattice Models for Grothendieck Polynomials (with Ben Brubaker, Claire Frechette, Emily Tibor, and Katherine Weber), Algebr. Comb. 6, no. 3, 789-–833 (2023).
- Arborescences of Covering Graphs (with Sunita Chepuri, CJ Dowd, Gregory Michel, Sylvester Zhang, and Valerie Zhang), Algebr. Comb. 5, no. 2, 319-–346 (2022).
- Characters of Renner Monoids and Their Hecke Algebras (with Jared Marx-Kuo, Vaughan McDonald, John O'Brien, and Alex Vetter), Int. J. Algebra Comput. 30, no. 7, 1505--1535 (2020).
- Restricted Symmetric Signed Permutations (with Justin Troyka), Journal of Pure Math and Applications 23, 179--217 (2012). Slides.
Other Documents
- Algebraic Operations via Solvable Lattice Models, University of Minnesota Ph. D. Dissertation, 2022.
- Finite Hecke Algebras and Their Characters, University of Minnesota Mathematics Oral Exam Paper, 2019.
- Combinatorial Species and Graph Enumeration (with Pete McNeely, Tung Phan. and Justin Troyka), Carleton College Undergraduate Senior Thesis.
Conferences/Seminars Organized
- UIUC Algebra-Geometry-Combinatorics Seminar, 2023-2025, with (subsets of) Ian Cavey, Shiliang Gao, David Keating, Elizabeth Kelley, and Alexander Yong (Fall 2023, Spring 2024, Fall 2024, Spring 2025, Previous years)
- Summer School in Combinatorial Representation Theory, (2025), with Ian Cavey and Alexander Yong; and Summer School in Combinatorial Lie Theory, (2024), with Alexander Yong
- UIUC Early-Career Combinatorics Conference, June 2024, with Jozsef Balogh, Peter Bradshaw, Ian Cavey, Elizabeth Kelley, Ethan White, Michael Wigal, and Alexander Yong
- Special Session on Solvable Lattice Models and their Applications, Joint Mathematics Meetings, January 2024, with Amol Aggarwal, Ben Brubaker, Daniel Bump, Slava Naprienko, Leonid Petrov, and Anne Schilling
- UIUC Schubert Calculus Summer School, June 2023, with Reuven Hodges, Elizabeth Kelley, Avery St. Dizier, and Alexander Yong.
- Minnesota Student Number Theory Seminar, 2019-20, with Joe Dickinson
Applets
- Quiver loci multiplicities (based on joint work with Ian Cavey and Alexander Yong, ArXiv:2608.06664)