| Résume | Since their introduction in the eighties, the study of the moduli space of (pseudo)-holomorphic curves, and in particular the Gromov-Witten invariants extracted from them, have been a very powerful tool in symplectic geometry and topology. Motivated by string theory considerations, Gopakumar and Vafa conjectured that the Gromov-Witten invariants of Calabi-Yau 3-folds satisfy some surprising properties. In earlier joint work with Thomas Parker and more recently with Aleksander Doan and Thomas Walpuski we proved a structure theorem for these invariants which implies the Gopakumar-Vafa conjecture.
This talk presents some of the background and key ingredients of our proof, as well as recent progress, joint with Penka Georgieva, towards proving that a similar structure theorem holds for the real Gromov-Witten invariants of Calabi-Yau 3-folds with an anti-symplectic involution. |
