Mingyuan Hu - Skein valued open Gromov-Witten invariants and cluster mutations

Mingyuan Hu (Northwestern University); September 12, 2024

We consider a class of Lagrangians living in \mathbb{C}^3 . Their Ekholm-Shende wavefunctions, living in the HOMFLY-PT skein module, will encode open Gromov-Witten invariants in all genus and with arbitrary numbers of boundary components. We develop a skein valued cluster theory to compute these wavefunctions. In the case of Aganagic-Vafa brane, our computation matches up with the prediction of the topological vertex. We also define a skein-valued dilogarithm and prove a pentagon relation, which will imply the 5-term relation of Garsia and Mellit. This talk is based on arXiv:2312.10186 (joint with Gus Schrader and Eric Zaslow) and arXiv:2401.10817.