My Research

Here I will attempt to explain my research over the course of (possibly many) posts.

Here's the short version first:

Cluster algebras are algebras that exhibit a particular struture that is in some sense very combinatorial. People care about these for various reasons. A Grassmannian is a collection of subspaces of some space that all have the same dimension. Such a collection forms a 'variety' which makes geometers happy. People also care about these for various (typically diferent) reasons.

If you happen to live in the intersection of these two groups of people, then boy are you in luck. It turns out that the algebra of functions on a Grassmannian enjoys a cluster structure. My research revolves around trying to understand this structure through the means of categorification. Specifically, a particular category constructed by Jensen, King and Su.

• Cluster Algebras
• Grassmannians
• Cluster structure on the coordinate ring of the Grassmannian
• Quiver Representations
• Categorification
• The category CMC

Categorification 13-11-24