Lagrangian-type Submanifolds of G2 and Spin(7) Manifolds
The study of Lagrangian submanifolds has played a fundamental role in furthering the field of symplectic geometry. Lagrangian submanifolds reveal information about Hamiltonian mechanics, symplectic rigidity, and local invariants of symplectic manifolds. Further, a deeper understanding of Lagrangian submanifolds has provided insight towards establishing a correspondence between Calabi-Yau mirror pairs in Kontsevich's homological mirror symmetry via the Fukaya category. In this talk, we discuss the analogues for Lagrangian submanifolds in G2 and Spin(7) geometry. We will discuss properties of these submanifolds as well as their deformation spaces. This is joint work with Sema Salur.