Appears in collection : Symmetry in Geometry and Analysis

Isoparametric hypersurfaces have their origin in geometric optics in Italy. They are fronts of light developing from some source. In Euclidean and hyperbolic spaces, these are just concentric spheres or cylinders. In contrast, in the sphere $S^{n+1}$, there are infinitely many non-homogeneous ones, corresponding to each representation of Clifford algebras.

Here we are interested in their image $L$ under the Gauss map. They are minimal Lagrangian submanifolds in the complex hyperquadric $Q_n(\mathbb C)$. We attack computing the Floer homology of $L$.

I’ll give an introductory talk as the subject may not be familiar to the audience.