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Explore the mathematical foundations of spin chain dualities in this lecture by Dr. Corey Jones from North Carolina State University, presented at the BIMSA-Tsinghua Quantum Symmetry Seminar. Learn about Kramers-Wannier style dualities as locality-preserving mappings between spin systems that create isomorphisms on observable subalgebras containing Hamiltonian terms. Discover how these abstract spin chains connect to subfactor theory and understand the classification of dualities up to internal finite-depth circuits. The talk covers important invariants from subfactor theory and presents a complete classification for symmetric operators under onsite finite group symmetry, based on research conducted with Kylan Schatz and Dominic Williamson. Dr. Jones, an assistant professor of Mathematics at NC State whose research spans quantum symmetries, tensor categories, subfactors, and operator algebras, delivers this comprehensive exploration of quantum mathematical structures.
