Chris Daw (University of Reading) – Elliptic curves, special points, and unlikely intersections

This will be a talk aimed at a wide audience. In the first part, I will recall the notion of an elliptic curve over the complex numbers and I will review the beautiful theory that allows us to classify them. Following this, I will recall what it means for an elliptic curve to have complex multiplication (CM) and I will discuss major advances over the last 30-40 years that describe how tuples of CM elliptic curves are distributed. Finally, I will venture into the realm of "unlikely intersections", which aims to study the distribution of other forms of "additional structure" on elliptic curves and their generalizations.