Research

Published/Accepted: 

1. Representations of free products of semisimple algebras via quivers, with Andrew Buchanan, Ivan Dimitrov, Olivia Grace, Charles Paquette, and David Wehlau. Journal of Pure and Applied Algebra, Volume 228, Issue 4 (2024), 24 pp. [journal] [arXiv]

2. 2-roots for simply laced Weyl groups, with Richard Green. Transformation Groups (2023), 42 pp. [journal] [arXiv]

3. Kazhdan–Lusztig cells of a-value 2 in a(2)-finite Coxeter groups, with Richard Green.  Algebraic Combinatorics, Volume 6 (2023) no.3, 46 pp. [journal] [arXiv]

4. Subregular J-rings of Coxeter systems via quiver path algebras, with Ivan Dimitrov, Charles Paquette and David Wehlau. Journal of Algebra, Volume 612 (2022), 51 pp. [journal] [arXiv]

5. Classification of Coxeter groups with finitely many elements of a-value 2, with Richard Green. Algebraic Combinatorics, Volume 3 (2020) no.2, 34 pp. [journal] [arXiv]

6. On the subregular J-rings of Coxeter systems. Algebras and Representation Theory, Volume 22, Issue 6, 2019, 34 pp. [journal] [arXiv]

7. Sandpiles and dominos, with Laura Florescu, Daniela Morar, David Perkinson, and Nick Salter. The Electronic Journal of Combinatorics, Volume 22 (1), 2015, 35 pp . [journal] [arXiv]

8. A note on the critical group of a line graph, with David Perkinson and Nick Salter. The Electronic Journal of Combinatorics, Volume 18 (1), 2011, 6 pp. [journal] [arXiv]

Preprint:

9. A partial order on antichains of fixed size, with Richard Green, 12 pp. Submitted. [arXiv]

10. On involutions of the infinite dihedral group, with Ivan Dimitrov, Charles Paquette and David Wehlau. 6 pp.  [arXiv]

In preparation:

11. Noncrossing and nonnesting bases of Macdonald representations, with Richard Green.

Contributions to SageMath: 

1. Fully commutative elements [SageTrac ticket] [Sage reference page]

2. Kazhdan–Lusztig basis and cells [SageTrac ticket][Sage reference page]

Python code (usable in SageMath):

 3. Generalized Temperley–Lieb algebras and diagrams [GitHub] [demo] [diagram gallery]