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Geometry and Topology Seminar

Friday, November 6, 2020
3:00pm to 4:00pm
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3-manifold invariants, G-equivariant TQFT, and complexity
Eric Samperton, Department of Mathematics, University of Illinois at Urbana-Champaign,

Let G be a finite group. G-equivariant TQFTs have received attention from both mathematicians and physicists, motivated in part by the search for new topological phases that can be used as the hardware for a universal quantum computer. Our goal will be to convey two complexity-theoretic lessons. First, when G is sufficiently complicated (nonabelian simple), 3-manifold invariants derived from G-equivariant TQFTs are very difficult to compute (#P-hard), even on a quantum computer. Second, no matter what finite group G one uses, a 3-dimensional G-equivariant TQFT can not be used for universal topological quantum computation if the underlying non-equivariant theory is not already universal. This talk is based on joint works with Greg Kuperberg and Colleen Delaney.

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