Georgia Institute of Technology College of Sciences

An elliptic curve is the set of solutions to a cubic equation in two variables and it has a natural group structure---you can add two points to get another. I'll explain why this is so, give some examples of the different types of groups that can arise (depending on the ground field), and mention some recent results on curves with many points. The are some nice thesis problems in this area which will be discussed in a follow-up talk later this semester in the algebra seminar.