Title: Enumerative invariants of certain noncommutative Calabi-Yau threefolds
Abstract: In joint works with Klemm, Schimannek, and Sharpe; and with Schimannek, we used mirror symmetry and B-model techniques of physics to compute topological string amplitudes associated to singular double covers of P^3, which did not have a precise geometric interpretation. In this talk, I extend the mathematical theory of Gopakumar-Vafa invariants of Calabi-Yau threefold using perverse sheaves of vanishing cycles proposed by Maulik and Toda to a class of noncommutative Calabi-Yau threefolds, describe noncommutative resolutions of the singular double covers mentioned above, and conjecture, with evidence, that the associated Gopakumar-Vafa-type invariants coincide with the topological string amplitudes which had been computed by methods of physics. This talk is based on joint work with Schimannek and joint work in progress with Colin Ingalls and Zijing Ye.
Eric Zaslow
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