On the Logarithmic CFT Structure of 2D Critical Percolation

Explore the logarithmic conformal field theory structure underlying two-dimensional critical percolation in this 55-minute mathematical lecture. Delve into how the large-scale behavior of 2D critical percolation connects to conformal field theory, particularly logarithmic CFT with its characteristic logarithmic singularities alongside standard power-law divergences. Examine the recent proof of conformal covariance for connection probabilities and understand its significance for proving the Delfino-Viti conjecture. Investigate asymptotic expansions interpreted as operator product expansions (OPEs) and discover the first rigorous demonstration of logarithmic singularities emergence. Learn about the percolation "energy" field and its logarithmic partner, gaining insight into the mathematical foundations that describe critical phenomena in statistical mechanics through the lens of conformal field theory.