Yoshihiro Ohnita:

Geometry of Lagrangian submanifolds related to isoparametric hypersurfaces

Abstract:

In this talk I shall provide a survey of my recent works and their environs on differential

geometry of Lagrangian submanifolds in specific Kaehler manifolds, such as complex projective spaces, complex space forms, Hermitian symmetric spaces and so on. I shall emphasis on the relationship between certain minimal Lagrangian submanifolds in complex hyperquadrics and isoparametric hypersurfaces in spheres. I shall discuss their properties and related problems

such as classification, Hamiltonian stability and Lagrangian intersection theory for the Gauss

images of isoparametric hypersurfaces. This talk is mainly based on my joint work with Hui Ma (Tsinghua University, Beijing).