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

- Series
- Algebra Seminar
- Time
- Tuesday, April 16, 2013 - 16:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Dick Gross – 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.