MSc Thesis (Imperial College London) — In progress, 2025.
Conducted under the supervision of George Boxer, focusing on p-adic Hodge theory and modular forms.
On Deformation of Perfectoid Purity in Gorenstein Domains — with B. Baily, K. Dovgodko, and A. Simpson.
We investigate when F-purity deforms from \( R/pR \) to a complete Gorenstein local ring \( R \) to perfectoid purity, a mixed-characteristic analog of F-purity. This work establishes a connection between vanishing of local cohomology in absolute integral closures and deformation of splinters.
[arXiv:2504.02966]
Some Applications of the Brenner–Monsky Quartic — with K. Dovgodko and A. Simpson.
In preparation, 2025.
We construct a two-parameter family of rings whose Hilbert–Kunz multiplicities vary in two parameters by taking Segre products of Monsky’s quartics and present a new counterexample to localization commuting with tight closure.
[Early Draft]
Examples of Lie Algebras with Specified Newton Polygons — with G. Alwan, K. Huang, T. Huang, and B. Stovall.
In preparation, 2025.
We determine all minimal Newton polygons for Lie Algebras of analytic vector fields over \( \mathbb{R}^n \) for \( n \leq 13 \), and provide bounds for such Newton polygons in arbitrary dimensions.