Birational Calabi-Yau's and Floer Cohomology

Speaker: Mark McLean
Affiliation: Stony Brook
01/21/21

Given two birational Calabi-Yau manifolds or orbifolds one can ask, how are their Gromov-Witten invariants related? I will explain two partial results that use Hamiltonian Floer theoretic techniques. The first result, joint with Ritter, gives an alternative proof of the generalized McKay correspondence for isolated quotient singularities. The second result proves that birational Calabi-Yau manifolds have the same small quantum products. Finally I will comment on possible further directions.