Title: Conic bundles over elliptic curves
Abstract: In this talk, we'll explore the arithmetic of conic bundles X → E over elliptic curves of positive Mordell-Weil rank over a number field k. We will consider questions regarding the distribution of the rational points of X by examining the image of X(k) inside of the rational points of the base elliptic curve E. In the process, we will mention a result on a local-to-global principle for torsion points on elliptic curves over the rationals. This is joint work with Masahiro Nakahara.