Mathematics Department Colloquium: Heuristics for elliptic curves

Colloquium | March 23 | 4:10-5 p.m. | 60 Evans Hall

 Bjorn Poonen, MIT

 Department of Mathematics

The set of rational points on an elliptic curve has the structure of a finitely generated abelian group, but many of the most basic questions about this group remain answered. For instance, Poincaré in 1901 implicitly asked whether there is a uniform upper bound on the number of generators required as one varies the elliptic curve, and this question is still open.

Inspired by the Cohen-Lenstra heuristics for class groups, we will give a heuristic that suggests that such a bound exists. This is joint work with Jennifer Park, John Voight, and Melanie Matchett Wood.