Dimers, webs, and local systems

Abstract: For a planar bipartite graph G equipped with a SLn-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. Time permitting, we will discuss some relations to Fock-Goncharov theory. This is joint work with Rick Kenyon and Haolin Shi.

mathematical physicsgeometric topology

Audience: researchers in the discipline

( video )

Geometry, Algebra and Physics at KIAS