Bi-Invariants of 3-Manifold Surface Algebras

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• Zhengwei Liu (Tsinghua University)
• Tuesday 27 June 2023, 10:00-11:00
• Seminar Room 1, Newton Institute.

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OASW05 - OAS Follow on: Operator Algebras: Subfactors and Applications

Jones introduced planar algebras in 1999, which has been generalized to surface algebras in 2019 by Liu. In this talk, we introduce an isotopy invariant partition function BIMSA for a/b-alternating colored 3-manifolds M with defects of surfaces S, lines L and vertices V, where L and V are labelled by objects and morphisms in a spherical fusion category C. BIMSA conceptually unifies various notions of C, such as the Drinfeld center Z©, Turaev-Viro TQFT as a-colored subtheory, Reshetikhin-Turaev TQFT as b-colored subtheory, higher Frobenius-Schur indicators, etc. BIMSA also provides fruitful computational tools, so that several remarkable results could be easily verified, such as TV©(M)=RT(Z©)(M). While considering the a-b duality as a Fourier duality, we recover various inequalities in Quantum Fourier Analysis, such as the positivity of Liu-Palcoux-Wu invariants etc. This is joint work with Shuang Ming, Yilong Wang and Jinsong Wu.

This talk is part of the Isaac Newton Institute Seminar Series series.

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