  We establish an explicit equivalence between the stationary sector of the
Gromov-Witten theory of a target curve X and the enumeration of Hurwitz
coverings of X in the basis of completed cycles. The stationary sector is
formed, by definition, by the descendents of the point class. Completed cycles
arise naturally in the theory of shifted symmetric functions. Using this
equivalence, we give a complete description of the stationary Gromov-Witten
theory of the projective line and elliptic curve. Toda equations for the
relative stationary theory of the projective line are derived.
