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

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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 2-Selmer groups of Jacobians of hyperelliptic
curves over Q, and see how they are related to orbit counting using
pencils of quadrics. Previous knowledge of Selmer groups is not required.