Hyperelliptic curve counting on abelian surfaces via the Shioda-Inose K3 and related ideas.

Abstract. In my thesis I proved a formula for counting hyperelliptic curves on polarized abelian surfaces whose proof relies on the crepant resolution conjecture. One alternative and promising method to produce this formula uses the so-called Shioda-Inose K3 surface of A. This is a K3 surface which is, in a sense, Hodge theoretically isomorphic to A. In this talk I will present this formula and go over current work which explains these ideas.