Zusammenfassung für den Vortrag am 23.08.2022 (14:00 Uhr)Colloquium of the Max Planck Institute
Laurent Côté (Harvard University, USA)
On the Lagrangian intersection problem
23.08.2022, 14:00 Uhr, MPI für Mathematik in den Naturwissenschaften Leipzig, E1 05 (Leibniz-Saal)
A guiding problem in symplectic geometry is the "Lagrangian intersection problem". This problem asks about the number of intersection points between certain smooth Lagrangian submanifolds in a symplectic manifold. It was originally promoted by V.Arnold, who was motivated by considerations from classical physics.
While the original version of the Lagrangian intersection problem is now rather well-understood, I will discuss recent work with Shaoyun Bai which initiates the study of the Lagrangian intersection problem for certain singular Lagrangian subsets (called "skeleta") which are important in symplectic geometry. Classical tools do not work in this context. Instead, we introduce new methods which are motivated by "quantum" geometry and homological mirror symmetry.