Holomorphic curves, boundaries, skeins, and recursion

https://hu-berlin.zoom.us/j/61339297016

I will explain how to define all genus open Gromov-Witten invariants for Calabi-Yau 3-folds.  The key idea is to count curves by their boundary in the skein modules of Lagrangians. Then I will prove the assertion of Ooguri and Vafa that the colored HOMFLYPT polynomials of a knot are exactly the counts of holomorphic curves in the resolved conifold with boundary on a Lagrangian associated to the knot.  In the process we will see the geometric origin of recursion relations for colored knot invariants.  This talk presents joint work with Tobias Ekholm.