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DTSTART:20190331T030000
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DTSTART:20181028T020000
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DTSTAMP:20260403T232954Z
UID:5b3b5421db538791789964@ist.ac.at
DTSTART:20190326T173000
DTEND:20190326T183000
DESCRIPTION:Speaker: Ewain Gwynne\nhosted by M. Beiglböck\, N. Berestycki\
 , L. Erdös\, J. Maas\nAbstract: It is an open problem to construct a metr
 ic on $\\gamma$-Liouville quantum gravity (LQG) for $\\gamma \\in (0\,2)$\
 , except in the special case $\\gamma=\\sqrt{8/3}$. Nevertheless\, the Hau
 sdorff dimension $d_\\gamma$ of the conjectural LQG metric is well-defined
  in the following sense. For a large class of approximations of $\\gamma$-
 LQG distances --- including random planar maps\, Liouville first passage p
 ercolation\, Liouville graph distance\, and the Liouville heat kernel --- 
 there is a notion of dimension (in terms of a certain exponent associated 
 with the model) and these exponents all agree with one another.I will give
  an overview of some recent progress on understanding $d_\\gamma$. In part
 icular\, I will discuss the relationships between different exponents\, th
 e proof the $\\gamma\\mapsto d_\\gamma$ is strictly increasing\, and new u
 pper and lower bounds for $d_\\gamma$. These bounds are consistent with (a
 nd numerically quite close to) the Watabiki prediction for the value of $d
 _\\gamma$ for $\\gamma \\in (0\,2)$. However\, in an extended regime corre
 sponding Liouville first passage percolation with parameter $\\xi  >2/d_2$
 \, or equivalently LQG with central charge greater than 1\, the bounds are
  inconsistent with the analytic continuation of Watabiki's prediction for 
 certain parameter values.Based on joint works with Jian Ding\, Nina Holden
 \, Tom Hutchcroft\, Jason Miller\, Josh Pfeffer\, and Xin Sun.
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:cpetz@ist.ac.at
SUMMARY:Ewain Gwynne: The fractal dimension of Liouville quantum gravity: m
 onotonicity\, universality\, and bounds.
URL:https://talks-calendar.ista.ac.at/events/1862
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