Intersection Rigidity of Fixed Point Loci of Anti-Symplectic Involutions

The Arnold-Givental conjecture asserts that given a symplectic manifold with an anti-symplectic involution, if the image of the fixed-point locus under a Hamiltonian diffeomorphism intersect the fixed-point locus transversely, them the number of intersection points is bounded from below by the 𝐹2 Betti number of fixed-point locus. I will explain a proof of this conjecture, which builds on translating the problem into an equivariant Hamiltonian orbit counting problem following an idea of Lu and our earlier work on integral Hamiltonian Floer theory. This is a joint work with Shelukhin, Wang, and Xu.