I am primarily interested in commutative algebra and its interactions with algebraic geometry, particularly on the relationship between the geometry of a variety and the syzygies of its embeddings into a weighted projective spaces and other toric varieties. Some questions I think about are

How is the positivity of an embedding into a weighted projective space reflected in its syzygies?

How are intrinsic/extrinsic geometry and syzygies connected for subvarieties of weighted projective spaces?

How are positivity, geometry, and syzygies related for line bundles on stacky curves?

How can we generalize useful homological algebra tools to multigraded/toric settings? 

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

Here's a word cloud of my current research statement: