Appears in collection : 2023 - T2 - WS1 - GAP XVIII: Homotopy algebras and higher structures

In this talk, we will introduce introduce the notion of symplectic micromorphisms. First, we will explain how various natural examples such as flows and symmetries in classical mechanics or Poisson structures in geometry can be expressed as special symplectic micromorphisms. Second, we will describe how Fourier integral operators can be used to quantize symplectic micromorphisms yielding quantum counterparts of these structures. (The ideas in this talk are based on works in collaboration with Alan Weinstein, Alberto Cattaneo, Igor Mencattini, and Friedrich Wagemann).