Heuristics for boundedness of ranks of elliptic curves

Bjorn Poonen, MIT
Fine Hall 314

The set of rational points on an elliptic curve E over Q has the structure of an abelian group, and in 1922 Mordell proved that this group is finitely generated. We present heuristics that suggest that there is a uniform upper bound on its rank as E varies over all elliptic curves over Q. This is joint work with Jennifer Park, John Voight, and Melanie Matchett Wood.