Sam Frengley


Email: stf32 (at) cam (dot) ac (dot) uk
Some of my code is available on my GitHub.

About me

Hi, I am a PhD student at the University of Cambridge. My supervisor is Tom Fisher.
I am originally from New Zealand and am currently funded by a Woolf Fisher Scholarship.

My research interests are in arithmetic geometry and number theory, including computational aspects.

Publications and preprints

An algorithm for efficient detection of (N,N)-splittings and its application to the isogeny problem in dimension 2,
    joint with Maria Corte-Real Santos and Craig Costello,
    preprint. [Abstract] [ePrint] [Code]

On 12-congruences of elliptic curves,
    preprint. [Abstract] [arXiv] [Code]

Congruences of elliptic curves arising from non-surjective mod N Galois representations,
    Mathematics of Computation 92 (2023), no. 339, 409-450. [Abstract] [arXiv] [Code]
    MR 4496970, Zbl 07603636, DOI 10.1090/mcom/3770

Slides

N-congruences between quadratic twists of elliptic curves,
    YRANT, August 2021. [Slides]

ℓ-adic Galois representations and Weil-Deligne representations,
    my talk from this reading group on automorphy lifting theorems. [Slides]

If you've seen me talk and there were no slides, send me an email and I can give you the notes I was working off.

Reading groups

Bhargava's proof of van der Waerden's conjecture,
    Michaelmas 2022. [Schedule]

Misc