Member Seminar

Speaker: Sunghyuk Park, CMSA

Title: Skein remain the same

Abstract: The count of holomorphic curves in a Calabi-Yau 3-fold ending on a Lagrangian is famously not deformation invariant, but Ekholm and Shende have shown that it can be made invariant by counting in the skein. Given a 3-manifold M and a branched cover arising from the projection of a Lagrangian 3-manifold L in the cotangent bundle of M, we use the skein-valued curve count to construct a map from the skein of M to that of L. When M and L are products of surfaces and intervals, deforming L within the space of Lagrangians yields a skein-valued lift of the Kontsevich-Soibelman wall-crossing formula. After all, the skeins remain the same. Based on joint work (arXiv:2510.19041) with Tobias Ekholm, Pietro Longhi, and Vivek Shende.