My research interest lies in Algebraic Geometry and Commutative Algebra. I am interested in the following topics:

• Positive characteristic birational geometry. 

• Multiplicity theory  and asymptotic invariants in commutative algebra.

• 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 Arithmetic of Hilbert-Kunz values, Preprint.

• Frobenius Rigidity and Perfectoid Towers in Mixed Characteristic with Sankhaneel Bisui and Rajat Kumar Mishra, Preprint.

• Boundedness of geometrically integral ε-klt del Pezzo surfaces with Shikha Bhutani, Submitted, 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.