Seminarium KMMF "Teoria Dwoistości"

Lie groupoids and their Morita equivalence classes (differentiable stacks) provide geometric models for singular spaces such as orbifolds, quotient spaces, and leaf spaces. Contact geometry, the odd-dimensional analogue of symplectic geometry, can be naturally studied in this context.In the past decade, Getzler’s notion of shifted symplectic structures on differentiable stacks has inspired major developments in derived and higher differential geometry. In the first part of the talk, we recall the definitions of Lie groupoids, their Morita equivalence, and differentiable stacks. In the second part, we introduce the notion of shifted contact structures on differentiable stacks, discuss their relation to shifted symplectic structures, and present several illustrative examples.The talk is based on a joint work with A. Tortorella and L. Vitagliano.