Series Title: On the arithmetic of hyperelliptic curves
Tuesday October 9th
Lecture 1: The rank of elliptic curves
50 Birge Hall
I will review why elliptic curves are somewhat special, define the rank of a curve over the rational numbers, and motivate the conjecture of Birch and Swinnerton-Dyer on the L-function. After stating what is known, I will briefly introduce a new method, due to Manjul Bhargava, for studying the average rank.