Speaker: Aleksey Zinger (Stony Brook University/IAS)

Title: Mirror Symmetry for Stable Quotients Invariants

Abstract: We describe a mirror formula for the direct analogue of Givental's J-function in the SQ theory. The mirror formula in the SQ theory is remarkably similar to that in the Gromov-Witten theory, but the former does not involve a change of variables. This suggests that the mirror map relating the GW-invariants to the B-model of the mirror is more reflective of the choice of curve counting theory on the A side than of mirror symmetry. The proof of the mirror formula in the Fano case is as in the GW-theory. On the other hand, the proof in the Calabi-Yau case consists of showing that it is a consequence of the Fano case. This is joint work with Y. Cooper.