Pawel Borowka Title: Hyperelliptic curves on abelian surfaces Abstract: The aim of the talk is to answer the question what kind of smooth hyperelliptic curves can be embedded in a general abelian surface. The motivation of such question is to generalise the case of genus 2 curves on principally polarised surfaces to non-principal ones. A simple comparison of Weierstrass points and two torsion points show that the only possible genera are 2, 3, 4 and 5. We will show the constructions that give the existence of such curves. For 2 and 3 the  constructions are classical, genus 4 is a joint work with Gregory Sankaran and genus 5 is a joint work with Angela Ortega.