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Explore the mathematical properties of integer-valued Gaussian free fields and their phase transitions in this 53-minute conference talk. Examine the fundamental localization/delocalization phase transition phenomenon in two dimensions, building upon the foundational 1981 work by Fröhlich and Spencer and recent developments by researchers including Lammers, van Engelenburg, Lis, Aizenman, Harel, Peled, and Shapiro. Learn about random interface models and investigate whether phase transitions persist when integer-valued Gaussian free fields are subjected to random disorder through supercritical Bernoulli bond percolation constraints on ℤ². Discover how constraining the field to take identical values at both ends of closed edges in percolation configurations affects the model's behavior, based on collaborative research with Diederik van Engelenburg and Christophe Garban.
