My field of research is number theory. More specifically, I'm interested in the following (closely related) areas:
- Special values of L-functions
- Cohomology of Galois representations and Iwasawa theory
- P-adic modular and automorphic forms
- Computational methods for automorphic forms
Euler systems notes
For an introduction to my research area, see the following lecture notes:
- Notes of Sarah's and my lectures on Euler systems and the Bloch–Kato conjecture at the 2021 Alpbach Summer School
- Notes and videos of our course on Euler Systems at the 2018 Arizona Winter School.
- Notes of my Euler Systems mini-course at the Iwasawa centenary conference, Tokyo, 2017
Sage and Magma scripts
Here is some Magma code (mostly by my collaborator Lassina Dembele) for calculating Hilbert modular forms of non-paritious weight over real quadratic fields.
Here is a Sage script for computing the Atkin-Lehner W_N operators on modular forms spaces.
Notes for a talk on Bernstein–Zelevinsky derivatives for the 2021 London study group
In spring 2014, Alex Bartel and I organised a study group on Galois cohomology; see here.
In summer 2011 I organised a study group on p-adic rigid analytic geometry; see here.
Notes and other junk
- Computing with algebraic automorphic forms (notes of my lectures at the 2011 Heidelberg summer school)
- Slides for my talk Calculating Automorphic Forms for Unitary Groups Using SAGE at the Sage Days 6 conference, 11/11/2007.
- Notes for my talk Approaches to computing overconvergent p-adic modular forms and the accompanying implementation presentation at the Heilbronn Institute workshop "Computing with automorphic forms", summer 2008
- Slides for my talk Calculating p-adic modular forms at Sage Days 16, 25/6/2009.
- A note on the norm of the Up operator
- A note on the norms of overconvergent eigenfunctions
- Attempts to factorise the U3 operator
- Study group talks:
- Cambridge things:
- General junk:
- A note on topological groups (in which I show that if G is compact and Hausdorff its conjugacy class space is Hausdorff in the quotient topology).
- An introduction to Burnside's algorithm for calculating character tables of finite groups.
- A short note on roots of cubic polynomials (published in volume 59 of Eureka (March 2008), the journal of the Cambridge undergrad maths society), in which I investigate when all of the roots of a complex cubic have the same absolute value. (Although this was motivated by my research on automorphic forms for unitary groups, the actual content is elementary.)