Abstract：

We are going to explain the three words in the title and how they’re related. To be more specific, we consider a class of Lagrangians in C^3. Their Ekholm-Shende wavefunctions live in the HOMFLY skein module, encoding open Gromov-Witten invariants in all genus and with arbitrary numbers of boundary components. We develop a skein theoretical cluster theory, prove that these wavefunctions are related to each other under "cluster mutation", and hence compute them. This is joint work with Gus Schrader and Eric Zaslow.