Current Research
The geometry of eigenvarieties, in particular the \(p\)-adic rigidity of certain refined non‑cuspidal automorphic Saito–Kurokawa representations of \(\mathrm{GSp}_4(\mathbb{A}_\mathbb{Q})\), in the sense that they cannot be interpolated in any nontrivial positive‑dimensional \(p\)-adic family, establishing a \(\mathrm{GSp}_4\) analogue of Bellaïche’s rigidity theorems for \(\mathrm{U}(2,1)\).
Past Projects
MSci Dissertation (UCL), 2024
The Weil Conjectures, supervised by Dr Dario Beraldo.
An expository project exploring the statements, proofs, and implications of the Weil Conjectures, with a focus on étale cohomology and (Hasse–Weil) zeta functions of varieties over finite fields, in particular for algebraic curves and Fermat hypersurfaces.
Undergraduate Research Summer Project (UCL), Summer 2023
An eight‑week project on mixed moments of \(L\)-functions assuming the Grand Riemann Hypothesis, supervised by Dr Ian Petrow and funded by the LMS. I analysed and adapted ideas of Rudnick, Soundararajan and Young to obtain upper bounds consistent with the conjectures of Keating and Snaith, proving a new result on the distribution of central values of \(L\)-functions attached to elliptic curves.
Second Year Summer Project (UCL), Summer 2022
A collaborative project on the binary Golay code, exploring its connections to sphere packing in 8 and 24 dimensions, the Leech lattice, and the Kissing Number Problem. We investigated links to Conway groups and the classification of finite simple groups, presenting our findings to faculty and students.