Persistence of Unknottedness of Lagrangian Intersections

This lecture from the IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar features Yin Li from Uppsala University discussing the persistence of unknottedness of Lagrangian intersections. Explore the double bubble plumbing, a Stein neighborhood of two Lagrangian 3-spheres that intersect cleanly along an unknotted circle in a 6-dimensional symplectic manifold. Learn about Li's proof that there is no Hamiltonian isotopy of the Lagrangian spheres in these Stein neighborhoods that would cause them to intersect along a circle knotted in either component, contrasting with what occurs under smooth isotopies. The proof employs exact Calabi-Yau structures on wrapped Fukaya categories to classify spherical Lagrangians in double bubble plumbings. This research represents joint work with Johan Asplund and was presented on March 28, 2025.