Symplectic Geometry Seminar

We show that skein valued counts of open holomorphic curves in a symplectic Calabi-Yau 3-fold with Maslov zero Lagrangian boundary condition are invariant under deformations and discuss applications (Ooguri-Vafa conjecture and simple recursion relations for the topological vertex). We then discuss the underlying polyfold perturbation scheme that allows for Gromov-Witten counts of bare curves, i.e. leaving area zero curves unperturbed, where the key ingredient is the observation that ghost bubbles leave traces on bare curves in combination with estimates on the failure of the existence of forgetful maps. The talk reports on joint work with V. Shende.