My research interests mostly fall around the (mod p and p-adic) Langlands programme. That is, I enjoy thinking about Galois representations and automorphic forms. In particular, I am interested in understanding them (and connections between them) using algebraic geometry - especially in positive and mixed characteristic.
Young Researchers in Algebraic Number Theory (Y-RANT) - University of Oxford, 31st July - 2nd August 2024 - https://y-rant.github.io/
The Weight Part of Serre's Conjecture - Supervised by Prof Fred Diamond - [pdf]
Mod p Geometric Hilbert Modular Forms and their Galois Representations- Joint with Calle Sönne, supervised by Dr George Boxer - [in progress]
Local Moduli of Abelian Varieties and the Serre-Tate Theorem - [pdf].
This essay - supervised by Dr Rong Zhou - was at least partly responsible for sparking my current interests.
The content is expository: I claim no originality for the material.
As an undergraduate, I completed two summer research (SRIM) projects in the Centre for Mathematical Sciences, Cambridge. These were:
Quaternion Orders and Bruhat-Tits Trees - Supervised by Dr Amitay Kamber. On a construction of Lubotsky-Phillips-Sarnak, investigating orbit sizes of certain arithmetic groups acting on Bruhat-Tits trees.
Group Stability in Permutations - Supervised by Dr Oren Becker. Looking into notions of (in)stability in permutations for groups and their interaction with some standard constructions.
I have included these here to promote summer research for undergraduates. This is a great opportunity to try out research, and is great fun! I gained a lot from my experience on the programme, and would be happy to speak to students who would like to know more.