Number Theory seminar

Jerry Wang, Harvard University

"Pencils of quadrics and 2-Selmer groups of Jacobians of hyperelliptic curves"

Since Bhargava and Shankar's new method of counting orbits, average orders of the 2,3,4,5-Selmer groups of elliptic curves over Q have been obtained. In this talk we will look at a construction of torsors of Jacobians of hyperelliptic curves using pencils of quadrics and see how they are used to compute the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves over Q with a rational (non-)Weierstrass point.