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SUMMARY:André Henriques (University of Oxford)
DTSTART:20200925T160000Z
DTEND:20200925T170000Z
DTSTAMP:20260423T024658Z
UID:TQFT/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TQFT/11/">Re
 ps of relative mapping class groups via conformal nets</a>\nby André Henr
 iques (University of Oxford) as part of Topological Quantum Field Theory C
 lub (IST\, Lisbon)\n\n\nAbstract\nGiven a surface with boundary Σ\, its r
 elative mapping class group is the quotient of Diff(Σ) by the subgroup of
  maps which are isotopic to the identity via an isotopy that fixes the bou
 ndary pointwise. (If Σ has no boundary\, then that's the usual mapping cl
 ass group\; if Σ is a disc\, then that's the group Diff(S¹) of diffeomor
 phisms of S¹.)\n\nConformal nets are one of the existing axiomatizations 
 of chiral conformal field theory (vertex operator algebras being another o
 ne). We will show that\, given an arbitrary conformal net and a surface wi
 th boundary Σ\, we get a continuous projective unitary representation of 
 the relative mapping class group (orientation reversing elements act by an
 ti-unitaries). When the conformal net is rational and Σ is a closed surfa
 ce (i.e. ∂Σ = ∅)\, then these representations are finite dimensional 
 and well known. When the conformal net is not rational\, then we must requ
 ire ∂Σ ≠ ∅ for these representations to be defined. We will try to 
 explain what goes wrong when Σ is a closed surface and the conformal net 
 is not rational. <br>\n\nThe material presented in this talk is partially 
 based on my paper arXiv:1409.8672 with Arthur Bartels and Chris Douglas.\n
LOCATION:https://researchseminars.org/talk/TQFT/11/
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