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Uniformization of random surface and Liouville quantum gravity

Xin Sun, Columbia University
Tuesday, October 1, 2019 - 1:30pm to 3:20pm
PDL C-401
In the last two decades there has been huge advance in understanding random surface from the perspective of the scaling limit of random triangulations. In the first part of the talk we review some highlights in this direction.  In particular, we will explain in what sense the so-called Liouville quantum gravity is the uniformization of a class of natural random surfaces, and report a joint work with Nina Holden rigorously proving that pure Liouville quantum gravity is the scaling limit of uniform triangulation under a conformal embedding related to Smirnov's proof of Cardy's formula. In the second part of the talk, we explain some ingredients of the proof, including the theory of mating of trees and dynamical percolation.

This is a joint seminar with Rainwater Seminar. Please note the different time, location and format. The first part of 20-30 minutes is aimed at a non-expert audience including graduate students, followed by a break with coffee and cookies, The second part of the talk, about 45-50 minutes, can be aimed higher and more like a "regular" seminar talk.

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