Jack.ThorneAffiliation: University of Cambridge Title Of Talk: Arithmetic statistics and the heights of rational points
URLS: Abstract: Although computing the solutions to a given Diophantine equation is hard (!), families of equations often display striking statistical regularity -- this is the case, for example, for the family of Weierstrass elliptic curves over Q given by the equations $y^2 = x^3 + A x + B$, for which theorems of Bhargava--Shankar and Poonen--Rains give (respectively) exact formulae for the average size of certain Selmer groups and predictions for the distribution of the isomorphism type of the group. I will discuss recent progress in this area and new work that addresses the distribution not only of the number of rational points but their heights. (Joint work with Jef Laga.)
WARNING: This page contains MATH-JAX
Last update made Tue Mar 10 21:28:06 CDT 2026.
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