All of the words below will be explained in the talk.
Understanding the rank of an elliptic curve is a fundamental, but hard, problem. The dimension of the p-Selmer group gives an upper bound for the rank that is conjecturally the actual rank for almost all p. This talk will be a down-to-earth survey of the recent work of Friedlander, Iwaniec, Mazur and Rubin on spins. The upshot is that one can sometimes control the change in the 2-Selmer rank as we run through prime twists of an elliptic curve. A key technical input is Burgess' bound on character sums from the 60s.