Geometric Structures Laboratory

In this minicourse we try to relate higher Lie groupoids and their shifted symplectic structures with more classical concepts in Poisson geometry. We will begin by defining higher Lie groupoids from the simplicial point of view, and discuss their Morita equivalences and the higher analog of de Rham cohomology. We will then present shifted symplectic structures and lagrangians and discuss how hamiltonian actions and reduction fit in this framework. Throughout we will provide examples such as those produced by applying the Artin-Mazur $\overline{W}$ construction to double Lie groupoids (and in particular to strict 2-groups), and higher cotangent groupoids.

This will be the first talk in a mini-course. The talk will be about 50 minutes. The remainder of the time is meant for questions/discussion.