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SUMMARY:Dmitry Chelkak (École Normale Supérieure Paris and St. Petersbur
 g Dept. of Steklov Institute RAS)
DTSTART:20200601T120000Z
DTEND:20200601T130000Z
DTSTAMP:20260423T041353Z
UID:HSPETDS/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HSPETDS/12/"
 >Bipartite dimer model: Gaussian Free Field on Lorentz-minimal surfaces</a
 >\nby Dmitry Chelkak (École Normale Supérieure Paris and St. Petersburg 
 Dept. of Steklov Institute RAS) as part of Horowitz seminar on probability
 \, ergodic theory and dynamical systems\n\n\nAbstract\nWe discuss a new vi
 ewpoint on the convergence of fluctuations in the bipartite dimer model co
 nsidered on big planar graphs. Classically\, when these graphs are parts o
 f refining lattices\, the boundary profile of the height function and a la
 ttice-dependent entropy functional are responsible for the conformal struc
 ture\, in which the limiting GFF (and CLE(4)) should be defined. Motivated
  by a long-term perspective of understanding the `discrete conformal struc
 ture’ of random planar maps equipped with the dimer (or the critical Isi
 ng) model\, we introduce `perfect t-embeddings’ of abstract weighted bip
 artite graphs and argue that such embeddings reveal the conformal structur
 e in a universal way: as that of a related Lorentz-minimal surface in 2+1 
 (or 2+2) dimensions.\n\nThough the whole concept is very new\, concrete de
 terministic examples (e.g\, the Aztec diamond) justify its relevance\, and
  general convergence theorems obtained so far are of their own interest. S
 till\, many open questions remain\, one of the key ones being to understan
 d the mechanism behind the appearance of the Lorentz metric in this classi
 cal problem.\n\nBased upon recent joint works with Benoît Laslier\, Sanja
 y Ramassamy and Marianna Russkikh.\n
LOCATION:https://researchseminars.org/talk/HSPETDS/12/
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