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CATEGORIES:Probability
SUMMARY:Understanding Liouville quantum gravity through tw
o square subdivision models - Josh Pfeffer (MIT)
DTSTART;TZID=Europe/London:20191105T140000
DTEND;TZID=Europe/London:20191105T150000
UID:TALK131476AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/131476
DESCRIPTION:In my talk I will discuss a general approach to be
tter understand the geometry of Liouville quantum
gravity (LQG). The idea\, roughly speaking\, is to
partition the random surface into dyadic squares
of roughly the same ``LQG size''. Based on this a
pproach\, I will introduce two different models of
LQG that will provide answers to three questions
in the field: \n\n\n1) Rigorously explain the so-c
alled ``DDK ansatz'' by proving that\, for a surfa
ce with metric tensor some regularized version of
the LQG metric tensor $\\exp(\\gamma h) (dx^2 + dy
^2)$\, its law corresponds to sampling a surface w
ith probability proportional to $(\\det_{\\zeta}'
\\Delta)^{-c/2}$\, with $c$ the matter central cha
rge.\n\n\n2) Provide a heuristic picture of the ge
ometry of LQG with matter central charge in the in
terval $(1\,25)$. (The geometry in this regime is
mysterious even from a physics perspective.)\n\n3)
Explain why many works in the physics literature
may have missed the nontrivial conformal geometry
of LQG with matter central charge in the interval
$(1\,25)$ when they suggest (based on numerical si
mulations and heuristics) that LQG exhibits the ma
croscopic behavior of a continuum random tree in t
his phase.\n\n\nThis talk is based on a joint work
with Morris Ang\, Minjae Park\, and Scott Sheffie
ld\; and a joint work with Ewain Gwynne\, Nina Hol
den\, and Guillaume Remy.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Perla Sousi
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