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Description

A topic of current interest regards 'how often' a variety has a rational point. This topic was initially studied by Serre who gave upper bounds in the case of families of conics parametrised by a projective space. In the last few years this topic has been significantly enriched by Loughran and others. I will begin by giving an overview of the latest developments and finish by discussing joint work with Erik Visse, where asymptotics are given for a family of conics parametrised by arbitrary smooth hypersurfaces of low degree.