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SUMMARY:CLE Nesting and Liouville Quantum Gravity - Bertrand Duplantier (C
 EA/Saclay\; IHES)
DTSTART:20181025T140000Z
DTEND:20181025T150000Z
UID:TALK113023@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We describe recent advances in the study of Schramm-Loewner Ev
 olution (SLE)\, a canonical model of non-crossing random paths in the plan
 e\, and of Liouville Quantum Gravity (LQG)\, a canonical model of random s
 urfaces in 2D quantum gravity. The latter is expected to be the universal\
 , conformally invariant\, continuum limit of random planar maps\, as weigh
 ted by critical statistical models. SLE multifractal spectra have natural 
 analogues on random planar maps and in LQG. An example is extreme nesting 
 in the Conformal Loop Ensemble (CLE)\, as derived by Miller\, Watson and W
 ilson\, and nesting in the O(n) loop model on a random planar map\, as der
 ived recently via combinatorial methods. Their respective large deviations
  functions are shown to be conjugate of each other\, via a continuous KPZ 
 transform inherent to LQG.  Joint work with Gaetan Borot and J&eacute\;r&e
 acute\;mie Bouttier.
LOCATION:Seminar Room 1\, Newton Institute
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