BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Rémi Rhodes (Université Aix-Marseille) DTSTART:20210601T070000Z DTEND:20210601T080000Z DTSTAMP:20260423T005707Z UID:SPDEs/13 DESCRIPTION:Title: G luing random surfaces: conformal bootstrap in Liouville theory via Segal ’s axioms\nby Rémi Rhodes (Université Aix-Marseille) as part of St ochastic PDEs and their friends\n\n\nAbstract\nThe law of Markov processes indexed by time (the real line) take a simple form when expressed in term s of the action of the associated semigroup. The generalization of this qu estion to the case when the process is indexed by higher dimensional manif olds is more intricate and this question is particularly relevant in the s tudy of quantum field theories. A general proposal was formalized by G. Se gal in the eighties in this direction. Yet\, concrete examples of QFTs whe re the Segal axioms are indeed valid are extremely limited (beyond trivial cases). We treat here the case of a specific Conformal Field Theory (CFT) \, called the Liouville theory which is a probabilistic model of 2D random surfaces. The outcome is the validity of the conformal bootstrap\, i.e. a bridge between probability and representation theory: correlation functio ns are expressed in terms of (universal) holomorphic functions of the modu li parameters of the Riemann surface\, called conformal blocks which have a strong representation theoretical content\, and the structure constants of the CFT\, here the DOZZ formula. Conformal bootstrap was conjectured in physics in the eighties to be the universal structure of CFTs and Liouvil le theory is perhaps the first non trivial example where it can be shown t o hold mathematically. This talk will be introductory to these topics.\n LOCATION:https://researchseminars.org/talk/SPDEs/13/ END:VEVENT END:VCALENDAR