Publications | Ellis Caird

Research

This is where I'll say things about my research. Here is a rough idea of the kinds of things I work on/ am interested in:

Cluster algebras
Grassmannians
Representation theory (of associative algebras)
Categorification
Combinatorics - webs & dimers

Most recently, I am working towards classifying rigid indecomposable modules in additive categorifications of the cluster structure on the coordinate rings of Grassmannians. These are module categories introduced by Jensen, King, & Su that provide 'categorical lifts' of cluster variables, clusters, and mutation for Grassmannians. Cluster variables are in correspondence with rigid indecomposable modules.
The Grassmannians Gr(3,9) and Gr(4,8) are the only two (up to symmetry) of 'tame' or 'finite mutation' type, i.e. there are infinitely many cluster variables, but only finitely many quivers in its quiver mutation class. On the categorical side, this means that although there are infinitely many rigid indecomposable modules, they generally fall into understandable 1-parameter families.