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 differential operators.  Recently, I have been spending some time reading topics in birational geometry. 

My thesis topic is asymptotic colengths of families of ideals and multiplicity sequence associated to monomial ideals.

    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)

       1. Resurgence and asymptotic resurgence of GL-invariant ideals with Sankhaneel Bisui  and Alexandra Seceleanu. 

       2. Generalized Hilbert-Kunz multiplicity for families of ideals with Stephen Landsittel  (Draft available upon request).