General (Main) Seminar MSRI program on DDC-Heuristics for the arithmetic of elliptic curves

Organizer: V. Harizanov and A. Shlapentokh

For link contact [email protected]

Thursday, December 17, 12:00-1:00 ET on Zoom

Speaker: Bjorn Poonen, MIT

Title: Heuristics for the arithmetic of elliptic curves

Abstract: We discuss a probabilistic model for the arithmetic of elliptic curves, a model developed in a series of articles with Bhargava, Kane, Lenstra, Park, Rains, Voight, and Wood. We discuss the theoretical evidence for the model, and we make predictions about elliptic curves based on corresponding theorems proved about the model. In particular, the model suggests that all but finitely many elliptic curves over Q have rank <= 21, which would imply that the rank is uniformly bounded.