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SUMMARY:From Frobenius-Schur indicators to Kuperberg invariants - Yilong W
 ang (Beijing Institute of Mathematical Sciences and Applications)
DTSTART:20251106T100000Z
DTEND:20251106T113000Z
UID:TALK240313@talks.cam.ac.uk
DESCRIPTION:Frobenius-Schur indicators of spherical fusion categories are 
 powerful tools in the study of algebraic properties of 3D-TFTs. Inspired b
 y the close connections among (1) the Frobenius-Schur indicators of a semi
 simple Hopf algebra H\, (2) the Kuperberg invariant of lens spaces associa
 ted to H\, and (3) the Turaev-Viro invariants of lens spaces associated to
  the fusion category Rep(H)\, we investigate the Kuperberg invariants of f
 ramed 3-manifolds associated to general (not necessarily semisimple) Hopf 
 algebras. We show that the Kuperberg invariants of framed lens spaces are 
 categorical invariants\, and they naturally generalize Frobenius-Schur ind
 icators. The categorical invariance also holds for some other low-genus fr
 amed manifolds\, suggesting the potential existence of a categorical const
 ruction of the Kuperberg invariant in the nonsemisimple setting. This talk
  is based on joint work with Liang Chang and Siu-Hung Ng
LOCATION:Seminar Room 2\, Newton Institute
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