Broadly speaking, my research is in the representation theory of finite-dimensional algebras. In work related to my PhD thesis, I studied connections between the universal deformation rings of certain modules over a group algebra and fusion in group theory. This research program always concerns universal deformation rings, and may involve modular representation theory, homological algebra, group cohomology or special biserial algebras. Here are links to two papers connected to this research program.

Recently I have become interested in applying techniques from representation theory to problems in topological data analysis. I've proved some representation-theoretic analogues of algebraic stability theorems from persistent homology. Typically, the idea is to apply ideas from representation theory, like the Auslander-Reiten quiver, to study generalized persistence modules. Here are some papers in this research program.

In a current project, I'm trying to use something analagous to characters to separate different isomorphism classes of peristence modules and to quickly produce their barcode. I am also trying to generalize the results in "Tracking the variety of interleavings" to arbitrary (one-dimensional) persistence modules. This would provide a nice geometric interpretation of the the full collection of interleavings between two persistence modules