Equivariant Lagrangian Non-Displacements

Lagrangian Floer theory is useful to detect non-displaceability of Lagrangian submanifolds via Hamiltonian isotopies. A related question, in the presence of a group action, is whether a certain Lagrangian is equivariantly displaceable, that is by a Hamiltonian isotopy that commutes with a group action. I will address this question in certain settings where the group is ℤ2, the key example being S1

-invariant Lagrangians in ℂn, by developing a ℤ2-equivariant Floer cohomology in the spirit of Seidel's construction and computing it using Biran-Khanevsky's Floer-Euler class. This is joint work with Dylan Cant.