Broadly speaking, my research concerns the representation theory of finite-dimensional algebras.  In work related to my PhD thesis, I found connections between fusion in group theory and the universal deformation rings of certain modules over a group algebra.  This research involved modular representation theory, homological algebra and group cohomology.  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'm particularly interested in proving analogues of algebraic stability theorems from persistent homology for module categories of a poset algebra.  Here are links to two papers with my collaborator Killian Meehan, a PhD candidate at the University of Missouri.  

I am currently working on a project with two of my academic brothers where we are computing the versal deformation rings for the indecomposable modules of a symmetric special biserial algebra. 

 

I am also currently working with Killian to prove an algebraic stability theorem motivated by persistent homology that compares the interleaving distance to a metric induced by a weighted graph metric on the Auslander-Reiten quiver of a poset algebra of finite representation type.