  This article accompanies my June 1998 seminaire Bourbaki talk on Givental's
work. After a quick review of descendent integrals in Gromov-Witten theory, I
discuss Givental's formalism relating hypergeometric series to solutions of
quantum differential equations arising from hypersurfaces in projective space.
A particular case of this relationship is a proof of the Mirror prediction for
the numbers of rational curves on the Calabi-Yau quintic 3-fold. The approach
taken here is entirely algebro-geometric and relies upon a localization formula
on the moduli space of stable genus 0 maps to projective space. A different
proof of the quintic Mirror prediction may be found in the work of Lian, Liu,
and Yau.
