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