Dr Rachel Newton (University of Reading) gives a maths seminar at the School of Mathematics, UEA. The talk is on “Counting failures of a local-global principle”. The abstract is below.

Methods for solving polynomial equations in the integers and rationals have been sought and studied for more than 4000 years. Modern approaches try to piece together ‘local’ (meaning real and p-adic) information to decide whether a polynomial equation has a ‘global’ (meaning rational) solution. I will describe this approach and its limitations, with the aim of quantifying how often the local-global method fails within families of polynomial equations arising from the norm map between fields, as seen in Galois theory.

This is joint work with Tim Browning.