Overview
I am interested in algebraic combinatorics, with a focus on total positivity and cluster algebras. I am especially interested in how these ideas connect to other areas of mathematics and physics—particularly knot theory, statistical mechanics, and the physics of scattering amplitudes.
Research Focus
Algebraic combinatorics
Publications
- Amplituhedra and origami pdf (59 pages) | arXiv:2410.09574
- Positroids, knots, and q,t-Catalan numbers pdf (53 pages)joint with Thomas Lam
Duke Math. J., 173(11): 2117-2195, 2024 | arXiv:2012.09745 - Regularity theorem for totally nonnegative flag varieties pdf (63 pages)joint with Steven Karp and Thomas Lam
J. Amer. Math. Soc., 35(2): 513-579, 2021 | arXiv:1904.00527 - Ising model and the positive orthogonal Grassmannian pdf (49 pages)joint with Pavlo Pylyavskyy
Duke Math. J., 169(10): 1877-1942, 2020 | arXiv:1807.03282 - Braid variety cluster structures, II: general type pdf (29 pages) | arXiv:2301.07268
joint with Thomas Lam and Melissa Sherman-Bennett, submitted