Working Thesis Title
Explicit 16-descent on Elliptic Curves over Number Fields.
The method of descent for Diophantine equations involves deriving auxiliary equations which contains information on the solutions of the original equation. On elliptic curves n-descent refers to methods for computing the n-Selmer group, which comes down to finding local solutions of auxiliary curves called n-coverings. So far there are explicit algorithms for n-descent for elliptic curves over number fields when n = 2,4,8 among others. The main goal of my thesis is to construct an algorithm for 16-descent, which will be built upon the existing algorithms.
Supervisors:
Primary Supervisor: Brendan Creutz
Co-Supervisor: Felipe Voloch
Research Interests
Algebraic Geometry, Number Theory, Elliptic Curves, Algebraic Topology.
Academic History
- Master of Science (with Distinction), Mathematics, University of Canterbury, 2022.
- Bachelor of Science with Honours (with First Class Honours), Mathematics, University of Canterbury, 2020
- Bachelor of Science, Mathematics, University of Canterbury, 2019
Publications
Brendan Creutz, Sheng (Victor) Lu, The local-global principle for divisibility in CM elliptic curves, Pages 139-154, Volume 250, Journal of Number Theory (2023) DOI: 10.1016/j.jnt.2023.03.005
