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Rational Points on Curves

Prof. Victor Flynn, University of Oxford

Date Icon Week 1, Tuesday 13 October MT 2015
Time Icon 8:15pm

I shall consider the problem, given a curve with rational coefficients, of how one tries to find all of its rational points. I shall discuss various techniques, and explain how to solve a wide range of naturally occurring problems relating to: cycles of polynomials, Fermat quartics (including the recent solution of a challenge curve of Serre), a riddle of Diophantus, and part of the classification problem for Q-derived polynomials (a polynomial is Q-derived if it and all of its derivatives have all of their roots in Q).