Time: 9h, Wednesday, June 3, 2020

Location: Room 612, Building A6, Institutte of Mathematics and Google Meet https://meet.google.com/vha-ujbp-kwo

Abstract: In this talk, we prove a necessary condition when the equation $F(x^2,y^2,z^2)=0$ has a nontrivial solution in a cubic number field where $F(X,Y,Z)$ is a homogeneous quadratic form with rational coefficients. Then we use the necessary condition to study the family of curves $x^4+nx^2y^2+y^4=Dz^4$. This extends previous results by Cassels and Bremner.