AbstractGeneralized symmetries in two-dimensional spacetime are described by the algebraic structure of topological line defects. In particular, when the number of topological lines is finite, their algebraic structure is described by a fusion category or a superfusion category depending on whether the system is bosonic or fermionic. For this reason, finite generalized symmetries in 1+1 dimensi...
Abstract:Given a singularity with a crepant resolution, a symmetry of the derived category of coherent sheaves on the resolution may often be constructed. I discuss work in progress on general constructions of such symmetries for hypersurface singularities. This builds on previous results with Segal, and is inspired by work of Bodzenta-Bondal
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