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Title:
Most odd degree hyperelliptic curves have only one rational point

Speaker:
Bjorn Poonen

Abstract:
We prove that the probability that a curve of the form $y^2 = f(x)$ over $\mathbb Q$ with $\deg f = 2g + 1$ has no rational point other than the point at infinity tends to 1 as $g$ tends to infinity. This is joint work with Michael Stoll.

Link:
https://www.ias.edu/video/puias/2015/0326-BjornPoonen