A Mirror Theorem for Complete Intersection Orbifolds in Weighted Projective Spaces

The famous mirror formula for quintic threefolds, conjectured to Candelas, de la Ossa, Green, and Parkes, provides detail information on genus zero Gromov-Witten invariants of the quintic threefold. Mirror formula has been extended to larger classes of manifolds, e.g. nef complete intersections in toric manifolds (by the works of Givental, Lian-Liu-Yau, and others). Recent advance in orbifold theory has motivated a search for a mirror theorem for orbifolds. Such a generalization will be improtant for mirror symmetry in higher dimension, as one cannot insist on working with mainfolds by passing to crepant resoultions. In this talk we will discuss an approach to establish a mirror theorem for orbifolds, and explain such a mirror theorem for complete intersection orbifolds in weighted projective spaces.