Athens-Atlanta number theory seminar 1 - The arithmetic of hyperelliptic curves

Algebra Seminar
Tuesday, April 16, 2013 - 16:00
1 hour (actually 50 minutes)
Skiles 006
Harvard University
Hyperelliptic curves over Q have equations of the form y^2 = F(x), where F(x) is a polynomial with rational coefficients which has simple roots over the complex numbers. When the degree of F(x) is at least 5, the genus of the hyperelliptic curve is at least 2 and Faltings has proved that there are only finitely many rational solutions. In this talk, I will describe methods which Manjul Bhargava and I have developed to quantify this result, on average.