Heuristics for the Arithmetic of Elliptic Curves and Abelian Varieties

Explore a comprehensive overview of a probabilistic model for the arithmetic of elliptic curves in this one-hour conference talk. Delve into the theoretical evidence supporting the model, developed through collaborative efforts with Bhargava, Kane, Lenstra, Park, Rains, Voight, and Wood. Examine predictions about elliptic curves based on corresponding theorems proved within the model. Extend your understanding as the talk extrapolates these concepts to make predictions for higher-dimensional abelian varieties. Gain insights into cutting-edge research in algebraic geometry and number theory, presented by Bjorn Poonen at the ICBS2024 conference.