From subfactors to quantum information and backwards, at Vanderbilt University, Saturday, September 30, 2017

Shanks workshop: subfactors and applications

Abstract: We first talk about the applications of subfactor theory in quantum information. Inspired by a question in quantum information, we introduce surface algebras as an extension of planar algebras from the plane to surfaces. As an application, we give a new proof of the Verlinde formula for any modular tensor category (MTC) and any genus surface. We also prove new identities for MTCs including the 6j symbol self-duality. The proof is based on a recent result joint with Feng Xu, which identifies two different Fourier dualities...

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