In the late nineties st ring theorists Gopakumar and Vafa conjectured that the Gromov-Witten invariants of Calabi-Yau 3-fold s have a hidden structure: they are obtained\, by a specific transform\, from a set of more fundamen tal "BPS numbers"\, which are integers. In joint w ork with Tom Parker\, we proved this conjecture by decomposing the GW invariants into contributions of ``clusters" of curves\, deforming the almost co mplex structure and reducing it to a local calcula tion. This talk presents some of the background an d geometric ingredients of our proof\, as well as recent progress\, joint with Penka Georgieva\, tow ards proving that a similar structure theorem hold s for the real GW invariants of Calabi-Yau 3-folds with an anti-symplectic involution. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR