Intersection theory of Lagrangian submanifolds plays an important role to study symplectic topology. One efficient tool to study this comes from Lagrangian Floer (co)homology, which was first founded by Floer and generalized by Oh. The Floer cohomology ring of a Lagrangian submanifold is independent of the choice of the Hamiltonian isotropy. However, it seems that there are not many non-displaceable examples known yet.

In this program, we give attention to a very special and nice class of compact Lagrangian submanifolds embedded in complex hyperquadrics $Q_n(\mathbb{C})$. We know that the Gauss image, i.e. the image of the Gauss map of an isoparametric hypersurface in the unit standard hypersphere $S^{n+1}(1) \subset \mathbb{R}^{n+2}$ provides a compact minimal Lagrangian submanifold embedded in the complex hyperquadric $Q_n(\mathbb{C})([13,15,16])$. This program aims to study the Floer (co)homology of Gauss images and their Lagrangian intersection theory.