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SUMMARY:Understanding Liouville quantum gravity through two square subdivi
 sion models - Josh Pfeffer (MIT)
DTSTART:20191105T140000Z
DTEND:20191105T150000Z
UID:TALK131476@talks.cam.ac.uk
CONTACT:Perla Sousi
DESCRIPTION:In my talk I will discuss a general approach to better underst
 and the geometry of Liouville quantum gravity (LQG). The idea\, roughly sp
 eaking\, is to partition the random surface into dyadic squares of roughly
  the same ``LQG size''.  Based on this approach\, I will introduce two di
 fferent models of LQG that will provide answers to three questions in the 
 field: \n\n\n1) Rigorously explain the so-called ``DDK ansatz'' by proving
  that\, for a surface with metric tensor some regularized version of the L
 QG metric tensor $\\exp(\\gamma h) (dx^2 + dy^2)$\, its law corresponds to
  sampling a surface with probability proportional to $(\\det_{\\zeta}' \\D
 elta)^{-c/2}$\, with $c$ the matter central charge.\n\n\n2) Provide a heur
 istic picture of the geometry of LQG with matter central charge in the int
 erval $(1\,25)$. (The geometry in this regime is mysterious even from a ph
 ysics perspective.)\n\n3) Explain why many works in the physics literature
  may have missed the nontrivial conformal geometry of LQG with matter cent
 ral charge in the interval $(1\,25)$ when they suggest (based on numerical
  simulations and heuristics) that LQG exhibits the macroscopic behavior of
  a continuum random tree in this phase.\n\n\nThis talk is based on a joint
  work with Morris Ang\, Minjae Park\, and Scott Sheffield\; and a joint wo
 rk with Ewain Gwynne\, Nina Holden\, and Guillaume Remy.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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