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Explore advanced statistical mechanics concepts beyond traditional two-dimensional models in this comprehensive workshop series from the Institute for Pure & Applied Mathematics. Delve into cutting-edge research extending classical "integrable" statistical mechanics to higher dimensions and non-planar graphs through topics including graph limits, posets, multinomial models, random complexes, and random groups. Master common analytical tools such as random walks, graph Laplacians, homology theory, and determinants while examining Benjamini-Schramm limits of graphs, unimodular measures, spanning trees and complexes, chip firing/sandpile models, matroids, and higher determinantal processes. Investigate random complexes, multinomial models, random groups, rigidity theory, and statistical physics applications in dimensions greater than two through expert presentations covering hierarchical percolation, random aggregation on complex planes, biased transpositions, 3D dimers, random constraint satisfaction problems, interacting Polya urns, epidemic modeling on large networks, spectral gap estimates, dynamical last passage percolation, minimal surfaces in random environments, homological percolation, scaling limits of loop-erased random walks, Poisson-Dirichlet distributions, activated random walks, scaling exponents in stationary random graphs, branching random walks, arboreal gas theory, Radon-Nikodym topography, rigidity thresholds, and Potts lattice gauge theory.
