Friday, March 19, 2021
03/19/2021 - 1:00pm
We introduce a family of spaces called critical varieties. Each critical variety is a subset of one of positroid varieties in the Grassmannian. The combinatorics of positroid varieties is captured by the dimer model on a planar bipartite graph G, and the critical variety is obtained by restricting to Kenyon's critical dimer model associated to a family of isoradial embeddings of G. This model is invariant under square/spider moves on G, and we give an explicit boundary measurement formula for critical varieties which does not depend on the choice of G.