BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Gourab Ray (University of Victoria)
DTSTART:20201130T170000Z
DTEND:20201130T180000Z
DTSTAMP:20260423T024727Z
UID:QM3/23
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/QM3/23/">Uni
 versality of dimers via imaginary geometry</a>\nby Gourab Ray (University 
 of Victoria) as part of Quantum Matter meets Maths (IST\, Lisbon)\n\n\nAbs
 tract\nThe dimer model is a model of uniform perfect matching and is one o
 f the fundamental models of statistical physics. It has many deep and intr
 icate connections with various other models in this fiel\, namely the Isin
 g model and the six-vertex model.\n\nThis model has received a lot of atte
 ntion in the mathematics community in the past two decades. The primary re
 ason behind such popularity is that this model is integrable\, in particul
 ar\, the correlation functions can be represented exactly in a determinent
 al form. This gives rise to a rich interplay between algebra\, geometry\, 
 probability and theoretical physics.\nFor graphs with very regular local s
 tructures\, exact computations of the correlation functions are possible b
 y Kasteleyn theory. R. Kenyon pioneered the development of the subject in 
 this direction by proving that the fluctuations of the height function ass
 ociated to the dimer model on the square lattice converges to the Gaussian
  free field (a conformally invariant Gaussian field). However\, such compu
 tations seem only possible on graphs with special local structures\, while
  the dimer model is supposed to have GFF type fluctuations in a much more 
 general setting.\n\nIn this talk\, I will give an overview of an ongoing p
 roject with N\, Berestycki (U. Vienna) and B. Laslier (Paris—Diderot 7) 
 where we establish a form of universality about the GFF fluctuation of the
  dimer model. Our approach does not use Kasteleyn theory\, but uses a mapp
 ing known since Temperley—Fisher\, which maps the dimer model to uniform
  spanning trees. Remarkably\, as observed by Benjamini\, the “winding”
  of the branches of this spanning tree exactly measures the height functio
 n of the dimers. We combine this approach with the developing universal sc
 aling limit results of the uniform spanning trees\, revolutionized by Schr
 amm through the discovery of SLE. We show that the continuum ``winding” 
 of these continuum limiting spanning trees converge to the GFF and harness
  from this the universality of the scaling limit. A key input in identifyi
 ng the limit is the so-called imaginary geometry developed by Miller and S
 heffield. In a more recent work\, we extend this universality partially to
  general Riemann surfaces as well.\n\nThis talk is based on the following 
 preprints and some works in progress.\n\nhttps://projecteuclid.org/euclid.
 aop/1585123322 <br>\nhttps://arxiv.org/abs/1610.07994 <br>\nhttps://arxiv.
 org/abs/1908.00832\n
LOCATION:https://researchseminars.org/talk/QM3/23/
END:VEVENT
END:VCALENDAR