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SUMMARY:Remi Rhodes (Aix-Marseille)
DTSTART:20200424T150000Z
DTEND:20200424T160000Z
DTSTAMP:20260423T004757Z
UID:PatC/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/PatC/2/">Con
 formal Bootstrap in Liouville theory</a>\nby Remi Rhodes (Aix-Marseille) a
 s part of Probability and the City Seminar\n\n\nAbstract\nLiouville confor
 mal field theory (denoted LCFT) is a 2-dimensional conformal field theory 
 depending on a parameter $\\gamma\\in\\R$ and studied since the eighties i
 n theoretical physics. In the case of the theory on the Riemann sphere\, p
 hysicists proposed closed formulae for the n-point correlation functions u
 sing symmetries and representation theory\, called the DOZZ formula (when 
 n=3) and the conformal bootstrap (for n>3). A probabilistic construction o
 f LCFT was recently proposed by David-Kupiainen-Rhodes-Vargas for $\\gamma
  \\in (0\,2]$ and the last three authors later proved the DOZZ formula. In
  this talk I will present a proof of equivalence between the probabilistic
  and the bootstrap construction (proposed in physics) for the n point corr
 elation functions with n greater or equal to 4\, valid for $\\gamma\\in (0
 \,1)$. Our proof combines the analysis of a natural semi-group\, tools fro
 m scattering theory and the use of Virasoro algebra in the context of the 
 probabilistic approach (the so-called conformal Ward identities).\n\nBased
  on joint work with C. Guillarmou\, A. Kupiainen and V. Vargas.\n
LOCATION:https://researchseminars.org/talk/PatC/2/
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