eynard and orantin have recently defined invariants of any compact riemann surface equipped with two meromorphic functions, as a tool for studying enumerative problems in geometry. i will give a brief introduction to these invariants and describe a particular example that encodes the stationary gromov-witten invariants of the two-sphere. this brings new insight into the well-studied problem of the gromov-witten invariants of the two-sphere. conversely, we gain insight into the eynard-orantin invariants showing that in this example they are related to the landau-ginzburg model dual to gromov-witten invariants.