The Gopakumar-Vafa conjecture for symplectic manifolds
Duration: 1 hour 4 mins
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About this item
| Description: |
Ionel, E
Monday 14th August 2017 - 14:30 to 15:30 |
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| Created: | 2017-08-15 08:54 |
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| Collection: | Symplectic geometry - celebrating the work of Simon Donaldson |
| Publisher: | Isaac Newton Institute |
| Copyright: | Ionel, E |
| Language: | eng (English) |
| Abstract: | Co-authors: Thomas H Parker (MSU); Penka Georgieva (IMJ-PRG).
In the late nineties string theorists Gopakumar and Vafa conjectured that the Gromov-Witten invariants of Calabi-Yau 3-folds have a hidden structure: they are obtained, by a specific transform, from a set of more fundamental "BPS numbers", which are integers. In joint work with Tom Parker, we proved this conjecture by decomposing the GW invariants into contributions of ``clusters" of curves, deforming the almost complex structure and reducing it to a local calculation. This talk presents some of the background and geometric ingredients of our proof, as well as recent progress, joint with Penka Georgieva, towards proving that a similar structure theorem holds for the real GW invariants of Calabi-Yau 3-folds with an anti-symplectic involution. |
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