Title: Abelian TQFTs, codes, and holography
Abstract: In the first part, I will show how anyon condensation in 3D and 5D Abelian TQFTs naturally gives rise to both classical and quantum (error-correcting) codes, and I will then explain how codes emerge to describe the TQFT path integral on manifolds with boundary. In the second part, I will explain how 3D TQFTs can be consistently summed over all topologies, leading to a well-defined holographic dual. If time permits, I will conclude with a discussion of a mass formula that evaluates the number of topological boundary conditions from the partition function of TQFT gravity.
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