On the Arnold-Givental Conjecture

We present a proof of the Arnold-Givental conjecture on the number of intersection points between the fixed-point set of an anti-symplectic involution and its transverse Hamiltonian image. Our argument combines the methods of integral Floer theory, a reduction to Hamiltonian Floer cohomology due to Lu, and a new idea related to localization in an equivariant Floer theory tailored to the problem. This talk is based on a joint work with Shaoyun Bai, Yi Wang, and Guangbo Xu.