My research interest lies in commutative algebra and it's interaction with algebraic geometry. I am interested in the following topics:

•  Multiplicity theory, Hilbert-Kunz theory, and asymptotic invariants in commutative algebra.

•  Positive characteristic birational geometry.

•  Frobenius liftability and perfectoid methods in mixed characteristic.  

• Asymptotic colength for families of ideals: an analytic approach with Cheng Meng,  Journal of Algebra (2026) 822-889

arxiv.org;

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

• The multiplicity sequence of monomial ideals with Jonathan Montaño and Aniketh Sivakumar,  Submitted, arxiv.org.

• Transcendental Hilbert-Kunz multiplicities with Stephen Landsittel and Vinh Pham, Submitted  arxiv.org.

• Transcendental epsilon multiplicity via divisor volumes with Stephen Landsittel and Vinh Pham, Submitted, arxiv.org.

• Generalized Hilbert-Kunz multiplicity for families of ideals with Stephen Landsittel , Submitted,  arxiv.org.

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