Friday, December 08, 2017 at 5:00pm to 7:00pm
Speaker: Atticus Christensen
Title: Mordell-Weil Ranks of Elliptic Curves over Infinite Extensions of Q
Abstract: In this talk we will describe results which can be deduced using Iwasawa theory of elliptic curves. In particular, for fixed elliptic curve E defined over Q, we will discuss the growth of the rank of the finitely generated groups E(K) as K ranges over number fields contained in a fixed potentially infinite degree extension of Q. We will then explain how the conjectural behavior of certain L functions predicts some of these results.