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Explore the fascinating world of random tilings in this 54-minute lecture by Amol Aggarwal at BIMSA. Delve into the intricate geometry of lozenge tilings on the triangular lattice and discover how their local structures behave in large-scale limits. Examine microscopic correlations between individual tiles, investigate fluctuations along facet edges, and analyze the statistics of turning points within tilings. Learn about recent advancements in proving universality results for these statistics, demonstrating their occurrence under a wide range of boundary conditions. Gain insights into the mathematical principles underlying these complex tiling patterns and their implications for broader statistical phenomena.
