|Date: Monday, December 04, 2017
Location: 4096 East Hall (4:00 PM to 6:00 PM)
Title: Birational Calabi-Yau Manifolds have Isomorphic Hamiltonian Floer Cohomology Algebras
Abstract: We show that any two birational projective Calabi-Yau manifolds admit Hamiltonians with isomorphic Hamiltonian Floer cohomology algebras, after a certain change of Novikov rings. As a result, we show that such Calabi-Yau manifolds have isomorphic integral cohomology groups and also isomorphic small quantum cohomology rings after a change of Novikov rings. The proof is inspired by ongoing work of Borman and Sheridan and uses ideas from work by Groman, Venkatesh and Varulgunes. We construct Hamiltonians whose flow `wraps' around certain singular subvarieties of our Calabi-Yau manifolds and use them to construct a symplectic cohomology group. One then shows these respective symplectic cohomology groups are isomorphic.
Speaker: Mark McLean
Institution: Stony Brook