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

Series
Algebra Seminar
Time
Tuesday, April 16, 2013 - 4:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dick Gross – Harvard University
Organizer
Douglas Ulmer
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.