BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Uniqueness of the welding problem for SLE and LQG - Wei Qian (Univ
 ersity of Cambridge)
DTSTART:20180710T133500Z
DTEND:20180710T142000Z
UID:TALK107941@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Fix $\\kappa \\in (0\,8)$ and suppose that $\\eta$ is an SLE$_
 \\kappa$ curve in $\\mathbb{H}$ from $0$ to $\\infty$.  We show that if $\
 \varphi \\colon \\mathbb{H} \\to \\mathbb{H}$ is a homeomorphism which is 
 conformal on $\\mathbb{H} \\setminus \\eta$ and $\\varphi(\\eta)$\, $\\eta
 $ are equal in distribution then $\\varphi$ is a conformal automorphism of
  $\\mathbb{H}$.  Applying this result for $\\kappa=4$ establishes that the
  welding operation for critical ($\\gamma=2$) Liouville quantum gravity (L
 QG) is well-defined.  Applying it for $\\kappa \\in (4\,8)$ gives a new pr
 oof that the welding of two looptrees of quantum disks to produce an SLE$_
 \\kappa$ on top of an independent $4/\\sqrt{\\kappa}$-LQG surface is well-
 defined.  These results are special cases of a more general uniqueness res
 ult which applies to any non-space-filling SLE-type curve (e.g.\, the exot
 ic SLE$_\\kappa^\\beta(\\rho)$ processes). This is a joint work with Olive
 r McEnteggart and Jason Miller.
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR