My current research interests are in the singularities of the MMP in characteristic p and mixed characteristic, foundations of analytic geometry and $p$ -adic geometry, and computational algebraic geometry/number theory via the Julia programming language.

I've written a slightly longer description of my research for various audiences:

In preparation

GPU-accelerated zeta functions of projective hypersurfaces (with R. Batubara, Y. Huang, and M. Mellberg), in preparation

F

-intersection flatness of dagger and Berkovich affinoid algebras (with R. Datta and K. Tucker), in preparation

Preprints & Publications

Abhyankar valuations, Prüfer-Manis valuations, and perfectoid Tate algebras (with D. Dine), arXiv:2510.22678

F

-pure thresholds and quasi-

F

-purity of hypersurfaces (with V. Jagathese), arXiv:2509.06211

K3 surfaces of any Artin-Mazur height over

\mathbb{F}_5

and

\mathbb{F}_7

via Quasi-F-split singularities and gpu acceleration (with R. Batubara and A. Pan), arXiv:2502.12428

The perfectoid Tate algebra has uncountable Krull dimension, arXiv:2212.13315

The following publications come from pre-graduate-school projects, and might not reflect my current interests.

Leveraging Compiler Intermediate Representation for Multi- and Cross-Language Verification, (with M. S. Baranowski, S. He and Z. Rakamaric), Conference on Verification, Model Checking, and Abstract Interpretation. (2020) pdf

On the solvability of the discrete conductivity and Schrödinger inverse problems, (with J. Boyer and F. Guevara Vasquez), SIAM J. Applied Math. (2016) arXiv:1510.02848