I have been working on understanding the distribution of special loci in Shimura varieties in the p-adic setting, inspired by work of Herrero, Menares and Rivera-Letelier, who studied CM points in the modular curve . This first step in this is 'p-adic Equidistribution of Special Loci in a Product of Modular Curves' (arXiv link here), and I am currently thinking about extending this result to Orthogonal Shimura Variteies.
For my Qualifying Exam at Northwestern, supervised by Ananth Shankar, I studied about deformations of p-divisible groups using Grothendieck-Messing Theory, and applications of this to deformations of Abelian varieties.
Previously, I have thought about the Emerton-Gee Stack and the use of (Φ,Γ)-modules to classify Galois representations.
While I was a master's student in 2022, I wrote about Deforming Galois Representations under the supervision of Jack Thorne. My final essay is here.
In the summer of 2021, Parth Shimpi and I worked under the guidance of Dhruv Ranganathan on realising the ring of quasi-symmetric functions combinatorially as the Chow ring of a stack with a natural moduli interpretation. The slides from a talk we gave on this work are here.
A very very long time ago, in 2016, I visited CERN with a team from Colchester Royal Grammar School, which won a competition to perform an experiment there. This paper was the result.