Tuesday May 7th, 2024 | |
| Time: | 12:00 PM - 1:00 AM |
| Title: | Equivariant Lagrangian Floer Theory on Compact Toric Manifolds |
| Speaker: | Yao Xiao, Stony Brook University |
| Location: | Math 5-127 |
| Abstract: | |
| We define an equivariant Lagrangian Floer theory on compact symplectic toric manifolds for the subtorus actions. We prove that the set of Lagrangian torus fibers (with weak bounding cochain data) with non-vanishing equivariant Lagrangian Floer cohomology forms a rigid analytic space. We can apply tropical geometry to locate such Lagrangian torus fibers in the moment polytope. We prove, in certain cases, that the dimension of such a rigid analytic space is equal to that of the acting group. In addition, we apply equivariant theory to show that moment Lagrangian correspondences induced by symplectic reduction are unobstructed after bulk deformation, assuming the existence of certain equivariant Kuranishi structures and compatible equivariant CF-perturbations. | |