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SUMMARY:Antti Kupiainen (University of Helsinki)
DTSTART:20200612T160000Z
DTEND:20200612T170000Z
DTSTAMP:20260423T021401Z
UID:TQFT/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TQFT/6/">Int
 egrability of Liouville Conformal Field Theory</a>\nby Antti Kupiainen (Un
 iversity of Helsinki) as part of Topological Quantum Field Theory Club (IS
 T\, Lisbon)\n\n\nAbstract\nA. Polyakov introduced Liouville Conformal Fiel
 d theory (LCFT) in 1981 as a way to put a natural measure on the set of Ri
 emannian metrics over a two dimensional manifold. Ever since\, the work of
  Polyakov has echoed in various branches of physics and mathematics\, rang
 ing from string theory to probability theory and geometry.\nIn the context
  of 2D quantum gravity models\, Polyakov’s approach is conjecturally equ
 ivalent to the scaling limit of Random Planar Maps and through the Alday-G
 aiotto-Tachikava correspondence LCFT is conjecturally related to certain 4
 D Yang-Mills theories. Through the work of Dorn\,Otto\, Zamolodchikov and 
 Zamolodchikov and Teschner LCFT is believed to be to a certain extent inte
 grable.\n\nI will review a probabilistic construction of LCFT developed to
 gether with David\, Rhodes and Vargas and recent proofs of the integrabili
 ty of LCFT:\n\n-The proof in a joint work with Rhodes and Vargas of the DO
 ZZ formula\n(Annals of Mathematics\, 81-166\,191 (2020))\n\n-The proof in 
 a joint work with Guillarmou\, Rhodes and Vargas of the\nbootstrap conject
 ure for LCFT (arXiv:2005.11530).\n
LOCATION:https://researchseminars.org/talk/TQFT/6/
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