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Title:
Poisson AKSZ theories
Speaker:
Abstract:
I will describe a version of the AKSZ construction that applies to possibly-open source manifolds and to possibly-infinite-dimensional Poisson (as opposed to symplectic) target manifolds (the cost being that the target must be infinitesimal). Quantization of such theories has to do with the relationship between dioperads and properads, and to the fact (due to Merkulov and Vallette) that formality in one world does not imply formality in the other. In particular, universal quantization of AKSZ theories on R^d is equivalent to the formality of a certain properad which is formal as a dioperad. I will conjecture that it is also equivalent to formality of the E_d operad.
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