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Explore the mathematical foundations of the Villain model in dimensions greater than three through this 52-minute conference talk that examines massless phases and their relationship to celebrated phase transitions. Delve into the historical context of the XY and Villain models, which demonstrate the renowned Kosterlitz-Thouless phase transitions in two-dimensional systems. Learn about the spin wave conjecture, originally proposed by Dyson and by Mermin and Wagner, which predicts that spin correlations in these models at low temperatures closely relate to Gaussian free fields. Discover recent mathematical progress and developments for the Villain model in higher dimensions, building upon joint research with Paul Dario from CNRS. Gain insights into advanced statistical mechanics, phase transitions, and the mathematical techniques used to analyze these complex physical systems.
