Wall Crossings and Lagrangian Cobordisms

Abstract: We expect that two Lagrangian submanifolds have matching Floer theoretic invariants if they are related by a Hamiltonian isotopy. For example, an appropriately weighted count of Maslov index 2 disks with boundary on a Lagrangian L should remain unchanged under Hamiltonian isotopy. If the Hamiltonian isotopy is not very nice -- say that at some point the isotopy passes through a Lagrangian which bounds a non-regular Maslov index 0 disk -- then weights used to count the disks need to be corrected by a ``wall crossing transformation'' to obtain invariance. These transformations end up playing an important role in mirror symmetry, where they are the coordinate transformations used to build a mirror space from an SYZ fibration.

Lagrangian cobordisms give an equivalence relation on Lagrangian submanifolds which is weaker than Lagrangian isotopy, but is still expected to preserve Floer theory. In this talk, we look at a first example of a non-cylindrical Lagrangian cobordism providing an equivalence of Lagrangian Floer theory, and relate this to the story of wall-crossing arising from Hamiltonian isotopy.

Mathematics

Audience: researchers in the topic

Rutgers symplectic geometry seminar

Series comments: Please contact the organizers for zoom link Soham Chanda, Yuhan Sun, Chris Woodward