Abstract: I will discuss ongoing work on studying operator algebras in semiclassical gravity. In AdS/CFT, the large N limit of single-trace operators in the boundary CFT results in a type 3 von Neumann algebra. Including 1/N corrections promotes the algebra to type 2, which allows the von Neumann entropy to be defined and calculated. I will describe how this works for semiclassical perturbations around the microcanonical TFD state, and show that the von Neumann entropy agrees with the generalized entropy of the black hole.