QM Research Seminar: Skein Valued Cluster Theory and Open Gromov-Witten Invariants

For a Lagrangian submanifold living in Calabi-Yau threefold, Ekholm and Shende defined a wavefunction living in the HOMFLY-PT skein module of the Lagrangian, which encode open Gromov-Witten invariants in all genus and arbitrarily many boundary components. We develop a skein valued cluster theory to compute these wavefunctions for a class of Lagrangians in $\bC^3$.  Along the way we define a skein dilogarithm and prove a pentagon relation. We will also consider the Agangaic-Vafa brane in a class of toric Calabi-Yau threefolds. Part of this talk is based on joint works with Schrader, Zaslow and Shende.