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Delve into the fascinating world of dimer models and random tilings in this advanced mathematics lecture presented by Tomas Berggren from the Massachusetts Institute of Technology. Explore the intricate connections between perfect matchings on graphs and plane tilings using dominos and rhombi. Gain insights into Kasteleyn's theory, combinatorial correspondences with other models, and asymptotic methods for large-scale limits. Expand your understanding of probability measures on perfect matchings and their applications in geometry and statistical mechanics. Recorded at the Institute for Pure & Applied Mathematics (IPAM) at UCLA as part of the Geometry, Statistical Mechanics, and Integrability Tutorials, this 74-minute talk offers a deep dive into the mathematical foundations and analytical tools used to study these complex systems.
