Georgia Institute of Technology College of Sciences

I will review a little bit of the theory of algebric curves, which essentialy amounts to studying the zero set of a two-variable polynomial. There are several amazing facts about the number of points on a curve when the ground field is finite. (This particular case has many applications to cryptography and coding theory.) An open problem in this area is whether there exist "supersingular" curves of every genus. (I'll explain the terminology, which has something to do with having many points or few points.) A new project I have just started should go some way toward resolving this question.