# The Gopakumar-Vafa conjecture for symplectic manifolds

Presented by:
Eleny Ionel Stanford University
Date:
Monday 14th August 2017 - 14:30 to 15:30
Venue:
INI Seminar Room 1
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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