My main interests lie in commutative algebra of Noetherian local commutative rings. My results are almost all in the area of tight closure theory, which was developed by Hochster and Huneke starting in the late 1980's. For one, I have developed some additional scaffolding in phantom homology in order to show that Ian Aberbach's notion of phantom depth works well even for modules not of finite phantom projective dimension. More recently I extended classical work of Northcott and Rees, using recent work of Adela Vraciu on *-independence, to get good analogues of analytic spread for tight, plus, and Frobenius closures. This lead to an investigation of ''special parts of closures'' and a ``special Brian\,con-Skoda theorem'', still in progress.

Other than tight closure theory, I am very interested in homological dimensions, especially Gorenstein dimension and complete intersection dimension. I am also interested in a connection between invariant theory of binary forms with seminormality. Most recently, I am learning about the connections between relative test ideals in characteristic p algebra and multiplier ideals in algebraic geometry.