WorkshopsCounting embedded curves in Calabi-Yau threefolds and Gopakumar-Vafa invariants
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The Gopakumar-Vafa BPS invariant is an integer invariant of the cohomology of D-brane moduli spaces on Calabi-Yau threefolds in string theory. By a conjectured relationship to Gromov-Witten theory, it is expected that the invariant coincides with the "number" of embedded (pseudo-)holomorphic curves. In this talk, we will explain how the latter integer invariants can be defined for a generic choice of compatible almost complex structures. If time permits, we will comment on the corresponding analog to the open string case and some implications on the wall-crossing phenomenon and open questions towards complete solution to the Gopakumar-Vafa conjecture.
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Yong-Geun Oh
2011-07-05
11:00:00 - 12:00:00
R101 , Astronomy and Mathematics Building
The Gopakumar-Vafa BPS invariant is an integer invariant of the cohomology of D-brane moduli spaces on Calabi-Yau threefolds in string theory. By a conjectured relationship to Gromov-Witten theory, it is expected that the invariant coincides with the "number" of embedded (pseudo-)holomorphic curves. In this talk, we will explain how the latter integer invariants can be defined for a generic choice of compatible almost complex structures. If time permits, we will comment on the corresponding analog to the open string case and some implications on the wall-crossing phenomenon and open questions towards complete solution to the Gopakumar-Vafa conjecture.