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, particularly computational aspects.

Publications and preprints

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

  Congruences of elliptic curves arising from non-surjective mod N Galois representations,
    to appear in Mathematics of Computation. [Abstract] [arXiv] [Code]

Talks

  Congruences of elliptic curves arising from non-surjective Galois representations,
    Number theory seminar, University of Canterbury, January 2022.

  Congruences of elliptic curves arising from non-surjective Galois representations,
    Number theory seminar, University of Cambridge, November 2021.

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

Other Slides

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

Misc

• Some Magma I find useful sometimes:
  • Some code which relates LMFDB and Cremona labels in Magma.
  • It can be nice to automatically attach your personal intrinsics. This can be done with user startup specification files. You can e.g., create a ~/.global_spec spec file, followed by adding the command export MAGMA_USER_SPEC="~/.global_spec" to your .bashrc file.
  
  
• Check out Maths Craft, if you're based in New Zealand they run events, and in any case they have some fun resources.
  
  
• A record which remains standing from the first test match.