The purpose of this talk is to present an ongoing work on geometric quantization in the setting of shifted symplectic structures. I will start by recalling the various notions involved as well as the results previously obtained by James Wallbridge, who constructed the prequantized (higher) categories of a given integral shifted symplectic structure. I will then explain our main result so far: the construction of the shifted analogues of the Kostant–Souriau prequantum operators, which will be realized as a "Poisson module over a Poisson category" (a categorification of the notion of a Poisson module over a Poisson algebra). This will be obtained by means of deformation theory arguments for categories of sheaves in the setting of (derived) differential geometry. If time permits, I will discuss further aspects associated to the notion of polarizations of shifted symplectic structures.
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