Lie groupoids equipped with compatible symplectic structures (symplectic groupoids) play a central role in Poisson geometry; indeed, Poisson structures may be seen as infinitesimal versions of symplectic groupoids, in a way analogous to how Lie algebras correspond to Lie groups.
In this talk I will discuss how this picture extends to "higher" (multi/poly) symplectic geometry. As a result, we identify "higher" analogs of Poisson structures bearing a relation to "higher" symplectic forms that extends the way Poisson geometry generalizes symplectic geometry.