My research interest lies in commutative algebra and it's interaction with algebraic geometry. I like to think about topics related to blowup algebras, multiplicities, local cohomology, singularities in positive characteristic and toric geometry.  

Recently, I have been focusing on learning and applying techniques from birational geometry — both in characteristic zero and positive characteristic—as well as exploring aspects of geometric invariant theory.

    Publication(s) and Preprints 

1. Asymptotic colength for families of ideals: an analytic approach with Cheng Meng,  Submitted, arxiv.org;

2. Rational Powers, Invariant ideals and the summation formula with Sankhaneel Bisui, Jonathan Montaño, and Tài Huy Hà , Submitted,  arxiv.org.

3. A Volume = Multiplicity formula for p-families of ideals,  Proc. Amer. Math. Soc. 151. (2023), 4153-4161, arxiv.org.

Working project(s)

       Generalized Hilbert-Kunz multiplicity for families of ideals with Stephen Landsittel