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Seminar
FIELD Math:Analysis
DATE December 17 (Fri), 2021
TIME 15:00-16:00
PLACE Online
SPEAKER Park, Minjae
HOST Kang, Nam-Gyu
INSTITUTE MIT
TITLE Variational formula for Liouville quantum gravity
ABSTRACT Liouville quantum gravity (LQG) is a one-parameter family of random fractal surfaces conjectured to be the canonical continuous model of many important classes of discrete surfaces in statistical physics, string theory, and conformal field theory. In probability theory, the γ-LQG measure is rigorously defined in terms of regularizations, but the original motivation of LQG surfaces in string theory is based on the idea of weighting a manifold by some power of the “determinant of Laplacian”.

We construct a one-parameter family of approximate LQG surfaces justifying the heuristic definition in physics during the talk. For this, we derive a variant of the Polyakov-Alvarez variational formula using Brownian loops in non-smooth setting. Joint work with Morris Ang, Joshua Pfeffer, and Scott Sheffield.

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https://us02web.zoom.us/j/5258205033?pwd=SW41OGFyaFBDeFgrcFhTTVBkckYwZz09
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