The private life of Bryan

This talk will discuss the discovery of Heegner points from a historic perspective. They are a beautiful application of analytic techniques to the study of rational points on elliptic curves, which is now a ubiquitous theme in number theory. We will start with a historical account of elliptic curves in the 60's and 70's, and a correspondence between Birch and Gross, culminating in the Gross-Zagier formula in the 80's. Time permitting, we will discuss certain applications and ramifications of these ideas in modern number theory.