# The geometric distribution of ranks and Selmer groups over function fields

## Location

Math 384-I

Tuesday, November 12, 2019 4:00 PM

Aaron Landesman

Bhargava, Kane, Lenstra, Poonen, and Rains proposed heuristics for the distribution of arithmetic data relating to elliptic curves, such as their ranks, Selmer groups, and Tate-Shafarevich groups. As a special case of their heuristics, they obtain the minimalist conjecture, which predicts that $50\%$ of elliptic curves have rank $0$ and $50\%$ of elliptic curves have rank $1$. After surveying these conjectures, we will explain joint work with Tony Feng and Eric Rains, verifying many of these conjectures over function fields of the form $\mathbb F_q(t)$, after taking a certain large $q$ limit.