The AKSZ construction in derived algebraic geometry as an extended TQFT

The AKSZ construction, as implemented by Pantev-To ̈en-Vaqui ́e-Vezzosi inthe context of derived algebraic geometry, gives a symplectic structure on the derived stackof maps from an oriented compact manifold to a symplectic derived stack. I will describehow this gives rise to a family of extended topological field theories valued in highercategories of symplectic derived stacks, with the higher morphisms given by a notion ofiterated Lagrangian correspondences. This is joint work in progress with Damien Calaqueand Claudia Scheimbauer.