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Explore a mathematical lecture presenting a proof of a long-standing conjecture about the six-vertex model's convergence to the Gaussian Free Field (GFF). Discover how the six-vertex model functions as a height function model that unifies several two-dimensional statistical mechanics systems. Learn about the innovative proof methodology that combines techniques from multiple mathematical areas, featuring a soft analysis of the transfer matrix that notably avoids dependence on the Bethe Ansatz. Examine how this analysis is made rigorous through probabilistic tools, including the Fortuin-Kasteleyn-Ginibre (FKG) inequality and Russo-Seymour-Welsh (RSW) theory. Understand the collaborative research conducted with Hugo Duminil-Copin, Karol Kozlowski, and Ioan Manolescu. Investigate the closely related conjecture regarding Fortuin-Kasteleyn percolation associated with the six-vertex model and its potential convergence in the scaling limit to a Conformal Loop Ensemble, CLE(κ).
