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Sheldon Katz : Gopakumar-Vafa Invariants of Moduli Spaces of Holomorphic Curves and Integrality

In a remarkable paper, Gopakumar and Vafa have used M-theory to assign BPS invariants to families of holomorphic curves which are believed to yield the Gromov-Witten invariants. In this talk, techniques of algebraic geometry are developed for calculating these invariants which agree with mirror symmetry results in examples. The proper mathematical context for complete generalization of these ideas appears to require geometric invariant theory.

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