Quadrics in arithmetic statistics by Levent Alpoge
We introduce a trick that allows one to apply Bhargava's counting technique to count points on invariant quadrics. As an example application (on which the talk will focus) we prove that the average size of 2-Selmer groups of curves in the family y^2 = x^3 + B is 3 (a theorem of Ruth from his Princeton PhD thesis). The point of the whole thing is that the technique we introduce is quite insensitive to the quadric --- if there is time we will prove the same theorem for the much thinner family y^2 = x^3 + B^2 as well.