Research
My research focuses on representation theory and algebraic combinatorics, with applications in geometry, number theory, and physics. I am particularly interested in topics such as solvable lattice models, Schubert calculus, (non)symmetric functions, and the boson-fermion correspondence. Much of my work involves studying functions that generalize Schur polynomials, including supersymmetric Schur functions, Iwahori-Whittaker functions, Schubert and Grothendieck polynomials, along with various generalizations.
Papers Talks Conferences/Seminars Organized
Papers
- Stability of products of double Grothendieck polynomials (with David Wallach), 2025, preprint.
- When do Schubert polynomial products stabilize? (with David Wallach), 2024, preprint.
- Factorial Fock free fermions (with Daniel Bump and Travis Scrimshaw), 2024, preprint.
- Solving the n-color ice model (with many others), 2022, submitted for publication.
- Algebraic Operations via Solvable Lattice Models, University of Minnesota Ph. D. Dissertation, 2022.
- 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).
- Finite Hecke Algebras and Their Characters, University of Minnesota Mathematics Oral Exam Paper, 2019.
- Restricted Symmetric Signed Permutations (with Justin Troyka), Journal of Pure Math and Applications 23, 179--217 (2012). Slides.
- Combinatorial Species and Graph Enumeration (with Pete McNeely, Tung Phan. and Justin Troyka), Carleton College Undergraduate Senior Thesis.
Talks
- University of Toronto (will be 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)
- 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