# Most odd degree hyperelliptic curves have only one rational point

 Joint IAS/Princeton University Number Theory Seminar Topic: Most odd degree hyperelliptic curves have only one rational point Speaker: Bjorn Poonen Affiliation: Massachusetts Institute of Technology Date: Thursday, March 26 Time/Room: 4:30pm - 5:30pm/S-101 Video Link: http://video.ias.edu/puias/2015/0326-BjornPoonen

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.