This lecture by Richard Kenyon from Yale University explores the "multinomial dimer model" on graphs, focusing on the N-fold blow up of graphs where each vertex is replaced with N vertices and each edge with a complete bipartite graph K_{N,N}. Learn about the mathematical tractability of this model in the large N limit, including formulas for partition functions and limit shapes in various settings. Discover a three-dimensional version of the Aztec Diamond as part of this research, which was conducted in collaboration with Catherine Wolfram from Yale. Delve into this advanced mathematical topic presented at the Harvard Center for Mathematical Sciences and Applications.