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This talk is based on arXiv:2305.09451, arXiv:2403.18011 and work in progress. I will discuss several deformations of algebras which are closely related to $w_{1+\infty}$ and give bulk interpretations of the respective deformations. Some of these deformations arise naturally from a backreaction in self-dual Einstein gravity analogous to part of the recent top-down construction of Costello, Paquette and Sharma and I will highlight similarities and differences.