My research is in Commutative Algebra. Some keywords are: positive characteristic techniques, invariant theory, determinantal varieties, differential operators, linkage and residual intersections, local cohomology modules, Stanley--Reisner theory.
The arithmetic rank of the residual intersections of a complete intersection ideal
with Manav Batavia, Kesavan Mohana Sundaram, and Taylor Murray Preprint, 20 pp. [arXiv]
The arithmetic rank of determinantal nullcones
with Jack Jeffries, Anurag K. Singh, and Uli Walther Preprint, 52 pp. [arXiv]
Bounds on the plus-pure thresholds of some hypersurfaces in (ramified) regular rings
with Marta Benozzo, Vignesh Jagathese, Pedro Ramírez-Moreno, Karl Schwede, and Prashanth Sridhar Preprint, 22 pp. [arXiv]
Symbolic powers of the generic linkage of maximal minors
with Matteo Varbaro Preprint, 25 pp. [arXiv]
F-purity and the F-pure threshold as invariants of linkage Preprint, 23 pp. [arXiv]
On the natural nullcones of the symplectic and general linear groups
with Yevgeniya Tarasova and Uli Walther Journal of the London Mathematical Society, (2025).
[arXiv] [Journal]
Linkage and F-regularity of determinantal rings
with Yevgeniya Tarasova International Mathematics Research Notices, (2024).
[arXiv] [Journal]
When are the natural embeddings of classical invariant rings pure?
with Mel Hochster, Jack Jeffries, and Anurag K. Singh Forum of Mathematics, Sigma, (2023).
[arXiv] [Journal]
Counting geometric branches via the Frobenius map and F-nilpotent singularities
with Hailong Dao and Kyle Maddox Nagoya Mathematical Journal, (2024).
[arXiv] [Journal]
Homological properties of pinched Veronese rings
with Kyle Maddox Journal of Algebra, (2023).
[arXiv] [Journal]
Cohomological dimension of ideals defining Veronese rings Proceedings of the American Mathematical Society, (2021).
[arXiv] [Journal]