Abstract: For a planar bipartite graph G equipped with a SL(n)-local system, we show that the determinant of the associated Kasteleyn matrix counts “n-multiwebs” (generalizations of n-webs) in G, weighted by their web-traces. We use this fact to study random n-multiwebs in graphs on some simple surfaces. This is joint work with Rick Kenyon and Haolin Shi.
