An outline of shifted Poisson structures and deformation quantisation in derived differential geometry

Key Points

• This work aims to translate results from derived algebraic geometry to derived differential geometry, focusing on shifted Poisson structures.
• Discussed various structures including NQ-manifolds and smooth stacks.
• Examined existence and classification of deformation quantisations on these structures.
• Identified connections between shifted Poisson structures and deformation quantisations.
• Provided frameworks to categorize these structures in derived differential geometry.