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We construct a family of oriented extended topological field theories usingthe AKSZ construction in derived algebraic geometry, which can be viewed as analgebraic and topological version of the classical AKSZ field theories thatoccur in physics. These have as their targets higher categories of symplecticderived stacks, with higher morphisms given by iterated Lagrangiancorrespondences. We define these, as well as analogous higher categories oforiented derived stacks and iterated oriented cospans, and prove that allobjects are fully dualizable. Then we set up a functorial version of the AKSZconstruction, first implemented in this context byPantev-To\"en-Vaqui\'e-Vezzosi, and show that it induces a family of symmetricmonoidal functors from oriented stacks to symplectic stacks. Finally, weconstruct forgetful functors from the unoriented bordism $(\infty,n)$-categoryto cospans of spaces, and from the oriented bordism $(\infty,n)$-category tocospans of spaces equipped with an orientation; the latter combines with theAKSZ functors by viewing spaces as constant stacks, giving the desired fieldtheories.

The AKSZ Construction in Derived Algebraic Geometry as an Extended Topological Field Theory