I will review the construction of ''higher operations'' on local and extended operators in topological field theory, and some applications of this construction in supersymmetric field theory. In particular, the higher operation on supersymmetric local operators in a 3d N=4 theory turns out to be induced by the holomorphic Poisson structure on the moduli space of the theory. This leads to a new way of establishing the non-renormalization properties of this Poisson structure, and also to a simple topological reason for the appearance of its deformation quantization when the theory is placed in Omega-background. This is an account of joint work with Christopher Beem, David Ben-Zvi, Mathew Bullimore, and Tudor Dimofte.

**(Livestream from Perimeter Institute)**

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