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Title:
QK = GV for CY3 at g=0
Speaker:
Abstract:
In this talk, I will show that on a Calabi-Yau threefold (CY3) a genus zero quantum $K$-invariant (QK) can be written as a linear combination, preserving integrality, of a finite number of Gopakumar--Vafa BPS invariants (GV) with coefficients from an explicit multiple cover formula. Conversely, all Gopakumar--Vafa invariants can be determined by a finite number of quantum $K$-invariants in a similar manner. The technical heart is a proof of a remarkable conjecture by Hans Jockers and Peter Mayr. This result is consistent with the “virtual Clemens conjecture” for the Calabi–Yau threefolds. A heuristic derivation of the relation between QK and GV via the virtual Clemens conjecture and a “multiple cover formula” will also be explained. This is a joint work with You-Cheng Chou.
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