... formanipulating the sums (0.25). The operator calculus of the formalism is basicto the rest of the paper. In Sections 3 and 5, the formalism is applied to the Gromov-Witten theory of targets of genus 0 and ... equation4.1. The τ-function4.2. The string equation4.3. The Toda hierarchy5. The Gromov-Witten theory of an elliptic curveGROMOV-WITTEN THEORY, HURWITZ THEORY, AND COMPLETED CYCLES545We then find the ... theory, Hurwitz theory, and completed cycles By A. Okounkov and R. Pandharipande GROMOV-WITTEN THEORY, HURWITZ THEORY, AND COMPLETED CYCLES5350, ∞∈P1respectively. We will use the notation,µ,τki(ω),νP1,(1.5)to...