Critical varieties in the Grassmannian

Understand

We introduce a family of spaces called critical varieties.

• Each critical variety is a subset of one of the 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 $G$.