Dimers and 3-Webs

Richard Kenyon

This is joint work with Haolin Shi (Yale). 3-webs are bipartite, trivalent, planar graphs. They were defined and studied by Kuperberg who showed that they correspond to invariant functions in tensor products of SL_3-representations. Webs and “reduced” webs also occur naturally in the triple-dimer model. We show how various topological types of reduced webs in the triple-dimer model on a (potentially large) planar graph can be computed using Postnikov’s boundary measurement matrix.

https://www.ias.edu/video/dimers-and-3-webs