Constructing extended AKSZ topological field theories in derived symplectic geometry

Derived algebraic geometry and derived symplectic geometry in the sense of Pantev-Toen-Vaquié-Vezzosi allows for a reinterpretation/analog of the classical AKSZ construction for certain $\sigma$-models. It is given by taking mapping stacks with a fixed target building and describes ``semi-classical TFTs". Using the formalism of derived algebraic geometry as a blackbox, I will sketch how this construction yields extended TFTs, which involves harnessing many higher homotopies. This is joint work in progress with Damien Calaque and Rune Haugseng.