Pure Maths Colloquium: Rational solutions to polynomial equations in families
29 February 2016 16:00 in CM221
The search for rational solutions to polynomial equations is now ongoing for more than 4000 years. Modern approaches try to piece together 'local' information to decide whether a polynomial equation has a 'global' (i.e. rational) solution. I will describe this approach and its limitations, with the aim of quantifying how often the local-global method fails within certain families of polynomial equations defining twists of norm one tori. I will present work from two recent joint projects: one with Tim Browning, and the other with Christopher Frei and Daniel Loughran.
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