Descent algorithms for finding rational points on curves

Host Faculty: Engineering
General Subject Area: Pure Mathematics
Project Level: PhD
View the Research Website
FIND A PROJECT - Engineering

Which pairs of rational numbers x and y satisfy the equation 3x^3 + 4y^3 = 5? It turns out there are none, but this is not easy to prove. Descent is a method going back to Fermat which can be used to attack such questions. Nowadays with the help of computer algebra packages we can apply descent techniques much more broadly. The aim of this project to develop and implement algorithms for carrying out descent on new classes of equations such as pairs of quadratic equations in 3 variables. 


Supervisor: Brendan Creutz

Does the project come with funding


Final date for receiving applications



Number theory, algebra, geometry