Recorded 24 May 2024. Richard Kenyon of Yale University presents "On the higher-rank dimer model" at IPAM's Vertex Models: Algebraic and Probabilistic Aspects of Universality Workshop.
Abstract: On a planar bipartite graph with a GL(n) local system, we define an associated Kasteleyn operator and show that its determinant counts traces of “n-multiwebs”, which are combinatorial objects generalizing dimer configurations (which correspond to the case n=1). For SL(3) we compute connection probabilities in the scaling limit and show their conformal invariance. This is based joint works with Dan Douglas and Haolin Shi.
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