Title: Rational points on/near homogeneous hyper-surfaces
Abstract: How many rational points are on/near a compact hyper-surface? This question is related, for instance, to Serre's Dimension Growth Conjecture.
We survey the state of the art, and explain a standard random model. Furthermore, we report on recent joint work with Rajula Srivastava (Uni/MPIM Bonn).
Our arguments are rooted in Fourier analysis and, in particular, clarify the role of curvature in the random model.
Bao Le Hung
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