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
Papers
- 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, submitted for publication.
- Stability of products of double Grothendieck polynomials (with David Wallach), 2025, submitted for publication.
- 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.
Talks
- Schubert calculus stability, AMS 2025 Fall Central Sectional, Special session on Interactions between geometry, combinatorics, and flag varieties, St. Louis (October 2025)
- Multiplicities of quiver loci, AMS 2025 Fall Southeastern Sectional, Special session on Combinatorics and Geometry Related to Representation Theory, New Orleans (October 2025)
- Factorial Schur functions and the boson-fermion correspondence, AMS 2025 Fall Western Sectional, Special session on Geometry, Integrability, Symmetry, and Physics, Denver (August 2025)
- Schubert calculus stability, Schubert Seminar (March 2025)
- Solvable lattice models in cohomology and K-theory, University of Toronto Combinatorics Seminar (February 2025)
- Factorial Schur functions and the boson-fermion correspondence, University of Illinois Algebra-Geometry-Combinatorics Seminar, UIUC (October 2024)
- A factorial analogue of the boson-fermion correspondence (contributed talk), Quantum Groups and Representation Theory Conference in honor of Kailash Misra’s 70th birthday, NC State (October 2024)
- Solvable lattice models and the boson-fermion correspondence, Early-Career Conference in Combinatorics, UIUC (June 2024)
- Solvable lattice models for motivic Chern classes of Schubert cells, Trinity College, Conference on Solvable Lattice Models, Number Theory and Combinatorics Conference, Trinity College, Dublin (June 2024)
- Solvable lattice models and the boson-fermion correspondence, Purdue Mathematical Physics Seminar, Purdue (April 2024)
- Lattice models for motivic Chern classes of Schubert varieties, AMS-AWM Special Session on Solvable Lattice Models and their Applications Associated with the Noether Lecture, Joint Math Meetings, San Francisco (January 2024)
- Solvable lattice models and Grothendieck polynomials, University of Illinois Algebra-Geometry-Combinatorics Seminar, UIUC (August 2023)
- Solvable lattice models and the boson-fermion correspondence, Integrable Systems \& Symmetric Functions Workshop, University of Glasgow (March 2023, remote)
- (Super)symmetric Functions from Solvable Lattice Models and Discrete-Time Hamiltonian Operators, University of Minnesota Combinatorics Seminar (February 2022)
- Solvable lattice models from representations of quantum groups, Academia Sinica, Taipei (December 2021, remote)
- Hamiltonian Operators and Free Fermionic Lattice Models, Solvable Lattice Models Seminar (June 2021)
- Solvable Lattice Models, Statistical Mechanics, and Symmetric Functions, Carleton College Colloquium (June 2021)
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