About me

I'm a Graduate Teaching Assistant at King's College London. My research interests are in Computational Arithmetic Geometry, particularly genus 3 curves with a view towards the Birch–Swinnteron-Dyer Conjecture. Contact me at jordan.1.docking@kcl.ac.uk.

Published Research

• \(2^\infty\)-Selmer Partities via the Prym Construction
  Journal of Number Theory 265, 2024, pp. 208 – 265. (arxiv)
• Reduction of Plane Quartics and Dixmier–Ohno Invariants
  with Raymond van Bommel, Elisa Lorenzo García and Reynald Lercier
  Research in Number Theory 11 (41), 2025. (arxiv)
• Reduction of Plane Quartics and Cayley Octads
  with Raymond van Bommel, Vladimir Dokchitser, Elisa Lorenzo García and Reynald Lercier
  Foundations of Computational Mathematics, 2025. (arxiv)

Talks

• Stable Models of Genus Three Curves, Curves, Isogenies and BSD Study Group, 2022.
• Class Groups of Function Fields, Function Fields Study Group, 2021.
• Extracting Rank Information: Elliptic Curves and Beyond, Junior Number Theory Seminar, 2021.
• Non-hyperelliptic Genus 3 Curves, Aspects of Curves Study Group, 2021.
• Isogeny Invariance of the Birch–Swinnerton-Dyer Conjecture, BSD Conjecture Study Group, 2020.
• Notes on Galois Cohomology, Cohomology Study Group, 2020.
• Cassels' Proof of the Invariance of BSD Under Isogeny, Junior Number Theory Seminar, 2019.

PhD Thesis

Arithmetic of Curves of Genus Three and Their Jacobians. Supervised by Prof. Vladimir Dokchitser. Funded by EPSRC. Available (here)