Lagrangian Floer homology is an invariant associated to a Lagrangian L in a symplectic manifold. I will explain how the vanishing of this homology leads to interesting count of open Gromov Witten invariants of L. As this is not a symplectic seminar, quite some time will be spent on explaining all these notions.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/6043