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Explore how Liouville Quantum Gravity (LQG) advances the exact solvability of 2D statistical physics through this 50-minute mathematical lecture. Examine 2D percolation as a primary example to understand the recent breakthroughs in applying LQG to statistical physics problems. Discover the key innovation that distinguishes current applications from previous quantum gravity approaches based on the Knitznik-Polyakov-Zamolodchikov (KPZ) relation. Learn about the crucial interplay between exact solvability in Liouville conformal field theory and the coupling theory that connects LQG with Schramm-Loewner Evolution (SLE). Gain insights into how these mathematical frameworks work together to solve complex problems in 2D statistical physics that were previously intractable.
