In the 1990s, two physisists, Gopakumar and Vafa, proposed an ideal way to count curves in a Calabi-Yau threefold, that is conjecturally equivalent to other curve counting theories such as Gromov-Witten theory. It is very recent that Maulik and Toda gave a mathematically rigorous definition of GV invariants. In this talk, I will review a recent progress on the GV theory, including $\chi$-independence for GV invariants on local curves and degree two GW/GV equivalence for some smooth curves with generic normal bundles. This is based on a joint work with T. Kinjo and another work with B. Davison.
For further information about this zoominar, see: https://personal.math.ubc.ca/~jbryan/Zoominar-UBC-ETH/