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SUMMARY:The analytic backbone of the GFF/SLE coupling on Riemann surfaces 
 - Guillaume Baverez (University of Cambridge)
DTSTART:20200219T160000Z
DTEND:20200219T170000Z
UID:TALK139084@talks.cam.ac.uk
CONTACT:Renato Velozo
DESCRIPTION:This will be an introductory talk to Liouville Conformal Field
  Theory (LCFT) with an emphasis on its underlying geometric features. I wi
 ll start by reviewing some facts about Riemann surfaces (uniformisation\, 
 Teichmüller theory\, etc) and conformal welding\, which can be viewed as 
 a deformation of the pants decomposition of hyperbolic surfaces. Then I wi
 ll introduce the Gaussian Free Field (GFF) and Gaussian Multiplicative Cha
 os (GMC)\, the main probabilistic tools needed to construct the partition 
 function of LCFT. The latter is a mapping class group invariant function d
 efined on Teichmüller space and I will explain how it is possible to solv
 e a conformal welding problem involving GMC in order to construct this fun
 ction by induction on the Euler characteristic of the surface. Doing so\, 
 a natural probability measure arises on homotopy classes of simple closed 
 curves\, which is interpreted as a Schramm-Loewner Evolution (SLE).
LOCATION:MR14\, Centre for Mathematical Sciences
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