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.
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Supervisors:
Primary Supervisor:听Brendan Creutz
Co-Supervisor:听Felipe Voloch
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Research Interests
Algebraic Geometry, Number Theory, Elliptic Curves, Algebraic Topology.
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Academic History
- Master of Science (with Distinction), Mathematics, 蘑菇视频在线观看, 2022.听
- Bachelor of Science with Honours (with First Class Honours), Mathematics, 蘑菇视频在线观看, 2020
- Bachelor of Science, Mathematics, 蘑菇视频在线观看, 2019
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Publications
Brendan Creutz, Sheng (Victor) Lu,听,听Pages 139-154,听Volume 250,听Journal of Number Theory (2023)听DOI:听10.1016/j.jnt.2023.03.005听听
