A mirror theorem for the mirror quintic

A mirror theorem for the mirror quintic

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Mark Shoemaker, University of Michigan
Fine Hall 322

The celebrated Mirror Theorem of Givental and Lian-Liu-Yau states that the A model (quantum cohomology, rational curve counting) of the Fermat quintic threefold is equivalent to the B model (complex deformations, period integrals) of its mirror dual, the mirror quintic orbifold. In order for mirror symmetry to be a true duality however, one must also show that the B model of the Fermat quintic is equivalent to the A model of the mirror quintic. We prove such an equivalence by relating the orbifold Gromov-Witten theory of the mirror quintic to period integrals over a one parameter deformation of the Fermat quintic. This involves new calculations in orbifold Gromov-Witten theory.