Counting embedded curves in Calabi-Yau 3-folds using bifurcation analysis

I will report on joint work with Shaoyun Bai where we study bifurcations of embedded holomorphic curves in Calabi-Yau 3-folds in order to define an integer-valued invariant analogous to Taubes' Gromov invariant. We are able to understand the bifurcations completely in some cases and this results in the definition of an invariant which is conjecturally equivalent to Gopakumar-Vafa's BPS invariants. An interesting feature of the problem is that global virtual techniques don't seem to help so much and we instead need to build on a far-reaching generalization of usual generic transversality results due to Wendl.