The AKSZ construction in derived algebraic geometry as an extended topological field theory

The AKSZ construction, as implemented by Pantev-Toën-Vaquié-Vezzosi in the context of derived algebraic geometry, gives a symplectic structure on the derived stack of maps from an oriented compact manifold to a symplectic derived stack. I  will describe how this gives rise to a family of extended topological field theories, in the sense of symmetric monoidal functors from (∞, n)-categories of cobordisms to some target, which here is a higher category of symplectic derived stacks and iterated Lagrangian correspondences. This is joint work with Damien Calaque and Claudia Scheimbauer.