I am primarily interested in commutative algebra and its interactions with algebraic geometry and topology. 

Here is a word cloud of my most recent research statement. Some common themes include:

Nonstandard gradings and weighted projective space. There are many results connecting the algebra of standard graded polynomial rings and the geometry of varieties in projective space. I am interested in analogous connections between the geometry of varieties in weighted projective space and nonstandard graded polynomial rings.

Differential modules. In particular, I am interested in what happens when we try to generalize results about minimal free resolutions and free complexes to the setting of differential modules, and what this can teach us about the original results and structures.

Previous projects include work on dynamic complex networks and configuration spaces of graphs.