Derived symplectic geometry, part I

In the last few years, building on the establishment of a systematic theory of derived algebraic geometry, several mathematicians have begun to explore derived symplectic geometry. This work organizes and clarifies certain constructions and ideas coming from physics. In the first talk, we will explain what a symplectic derived stack is, describe a few nontrivial examples, and then discuss Lagrangians inside symplectic stacks. In the second talk, we will apply these ideas to some questions inspired by physics, notably to the construction of topological field theories (via Lagrangian correspondences and the AKSZ construction) and to categorical versions of deformation quantization.