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.