Researcher Information


Associate Professor

Turning fine mathematics into silly diagrams

Department of Mathematics, Mathematics


Combinatorial description of representation theory and Schubert calculus

FieldCombinatorial representation theory
KeywordCrystal basis, Yang-Baxter equation, Schubert calculus

Introduction of Research

Representation theory is about understanding symmetries of physical systems by studying algebraic objects using linear algebra. My research area seeks to describe representation theory in terms of combinatorial objects. Specifically, I focus on the representations of Kac-Moody Lie (super)algebras by using Kashiwara’s theory of crystals, which roughly describe what happens when the temperature in the system goes to zero. I have been applying these to Schubert calculus, which aims to understand the geometry of subspaces of a vector space, and exploring their connections to other areas, such as physics and probability theory.

Representative Achievements

Uniform description of the rigged configuration bijection, T. Scrimshaw, Selecta Math. (N.S.), 26(42) (2020).
Colored five-vertex models and Lascoux polynomials and atoms, V. Buciumas, T. Scrimshaw, and K. Weber, J. Lond. Math. Soc., 102(3) (2020) pp. 1047–1066.
Multiline queues with spectral parameters, E. Aas, D. Grinberg, and T. Scrimshaw, Comm. Math. Phys., 374(3) (2020) pp. 1743–1786.
Categorical relations between Langlands dual quantum affine algebras: Exceptional cases, S.-j. Oh and T. Scrimshaw, Comm. Math. Phys., 368(1) (2019) pp. 295–367.
Rigged configuration bijection and the proof of the X = M conjecture for nonexceptional affine types, M. Okado, A. Schilling, and T. Scrimshaw, J. Algebra 516 (2018) pp. 1–37.