  We compute the recently introduced Fan-Jarvis-Ruan-Witten theory of W-curves
in genus zero for quintic polynomials in five variables and we show that it
matches the Gromov-Witten genus-zero theory of the quintic three-fold via a
symplectic transformation. More specifically, we show that the J-function
encoding the Fan-Jarvis-Ruan-Witten theory on the A-side equals via a mirror
map the I-function embodying the period integrals at the Gepner point on the
B-side. This identification inscribes the physical Landau-Ginzburg/Calabi-Yau
correspondence within the enumerative geometry of moduli of curves, matches the
genus-zero invariants computed by the physicists Huang, Klemm, and Quackenbush
at the Gepner point, and yields via Givental's quantization a prediction on the
relation between the full higher genus potential of the quintic three-fold and
that of Fan-Jarvis-Ruan-Witten theory.
