Rotational Invariance of Planar Random Cluster Models and Beyond

Explore a cutting-edge lecture on rotational invariance in planar random cluster models presented by Hugo Duminil-Copin from The University of Geneva. Delve into the innovative technique introduced by Grimmett and Manolescu that revolutionized the understanding of critical exponents in planar bond Bernoulli percolation models. Discover how this star-triangle transformation-based strategy has been extended to broader random cluster models, particularly in demonstrating rotation invariance. Examine new possibilities arising from rotation invariance and gain fresh insights into critical random cluster models on Z^2. This 56-minute talk, recorded on May 22, 2024, is part of the Institute for Pure & Applied Mathematics (IPAM) workshop on Vertex Models: Algebraic and Probabilistic Aspects of Universality.