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Rahul Pandharipande : Integers in the Gromov-Witten Theory of 3-folds

Abstract: Gopakumar and Vafa have proposed a formula for the Gromov-Witten invariants of Calabi-Yau 3 folds in terms of numbers of BPS states. Part of this formula is explained by higher genus multiple covers and collapsed contributions in Gromov-Witten theory. The mathematical analysis leads to a direct generalization of Gopakumar and Vafa's formula to an integral structure for arbitrary 3 folds. I will discuss a mathematical approach to these questions via integrals over the moduli space of stable curves.

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