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Explore the fundamental concepts of random geometry in this comprehensive lecture on Gaussian free field (GFF) and Schramm--Loewner Evolution (SLE). Delve into the properties and applications of GFF, a rough version of a random harmonic generalized function, and its role in describing scaling limits of various statistical physics models. Discover the characteristics of SLE curves, their conformal invariance, and domain Markov property. Examine the intricate connections between GFF and SLE, including the relationship between zero-height level lines of GFF and SLE curves. Gain insights into the rigorous construction of Liouville conformal field theory and the significance of these concepts in quantum field theory and statistical mechanics.
