BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Guillaume Baverez (Humboldt-Universität zu Berlin) DTSTART:20230619T120000Z DTEND:20230619T130000Z DTSTAMP:20260423T024452Z UID:IPHT-PHM/28 DESCRIPTION:Title: Liouville theory: from Segal's axioms to conformal blocks\nby Guilla ume Baverez (Humboldt-Universität zu Berlin) as part of Séminaire de phy sique mathématique IPhT\n\nLecture held in Salle Claude Itzykson\, Bât. 774\, Orme des Merisiers.\n\nAbstract\nIn Segal's axiomatisation\, conform al field theories (CFT) can be constructed from (projective) representatio ns of the semigroup of annuli (the set of annuli with parametrised boundar ies endowed with the gluing operation). In the case of the Liouville CFT\, we realise this idea by defining a certain family of Markov processes on the space of distributions on the unit circle. Their generators exist as u nbounded operators on the Hilbert space and represent the Virasoro algebra (they are equivalent to the Sugawara construction). \nThis representation is instrumental in the study of the conformal blocks of the theory. We ca n define them using pants decomposition of the underlying surface\, and as sociate an operator in the Hilbert space to each pair of pants. The gluing of pairs of pants is represented by the composition of operators\, and th e conformal blocks are essentially the spectral decomposition of these ope rators. Their variation with respect to the complex structure of the surfa ce is governed by the semigroup\, which is a version of the statement that conformal blocks are horizontal with respect to the connection defined by the stress-energy tensor. This allows us to show that the blocks do not d epend on the choice of curves representing the pants decomposition. \nBase d on joint and ongoing works with Guillarmou\, Kupiainen\, Rhodes & Vargas .\n LOCATION:https://researchseminars.org/talk/IPHT-PHM/28/ END:VEVENT END:VCALENDAR