Wednesdays at 1:30pm (once a month)
Frank Adams 1, Alan Turing Building
Contacts Vahagn Aslanyan Yotam Smilansky
Rational points on algebraic curves
Martin Orr
University of Manchester
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.TBD
Valentina Disarlo
University of Manchester