Pure maths colloquium - Martin Orr

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Speaker: Martin Orr (University of Manchester) Title: Rational points on algebraic curves Abstract: Understanding rational solutions of polynomials in two variables is a classical theme in number theory. For example, Fermat's last theorem can be described in this way. In this talk, I will explain how this may be interpreted geometrically as the study of rational points on algebraic curves. I will describe some of the big historical results, including Mordell's famous theorem on elliptic curves and conjecture on higher-genus curves (dating from his time in Manchester). Then I will outline some more recent developments involving bounds for the number of rational points on curves, algorithms that (sometimes) find such points, and my own work on bounding the size of these points. The talk will be accessible to postgraduate students and will not assume prior knowledge about algebraic geometry or number theory. Room: Frank Adams 1 The talk will be followed by a reception.