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SUMMARY:Bi-Invariants of 3-Manifold Surface Algebras - Zhengwei Liu (Tsing
 hua University)
DTSTART:20230627T090000Z
DTEND:20230627T100000Z
UID:TALK201970@talks.cam.ac.uk
DESCRIPTION:Jones introduced planar algebras in 1999\, which has been gene
 ralized 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(C)\, Turaev-Viro TQFT as a-colored subtheory\, Reshetikhin-Turae
 v TQFT as b-colored subtheory\, higher Frobenius-Schur indicators\, etc. B
 IMSA also provides fruitful computational tools\, so that several remarkab
 le results could be easily verified\, such as TV(C)(M)=RT(Z(C))(M). While 
 considering the a-b duality as a Fourier duality\, we recover various ineq
 ualities in Quantum Fourier Analysis\, such as the positivity of Liu-Palco
 ux-Wu invariants etc. This is joint work with Shuang Ming\, Yilong Wang an
 d Jinsong Wu.
LOCATION:Seminar Room 1\, Newton Institute
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