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The dimer model is a statistical mechanical model that studies random dimer covers (perfect matchings) of a graph. Web categories are developed to compute the Witten-Reshetikhin-Turaev quantum invariants and to study the representations of quantum groups. 

Kasteleyn’s theorem computes the number of dimer covers of a graph by calculating the determinant of a modified adjacency matrix. The generalizations of the theorem connect generalized dimer models to type A web categories. I will talk about further generalizations to the type C cases, relaxing the bipartiteness condition of the underlying graph. This talk is based on joint work with Richard Kenyon.