Seminar Event Detail

Geometry & Physics

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

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