Critical Varieties in the Grassmannian

We introduce a family of spaces called critical varieties. Each variety is subset one the positroid varieties in Grassmannian. The combinatorics captured by dimer model on planar bipartite graph G, and obtained restricting to Kenyon’s associated isoradial embeddings G. This invariant under square/spider moves we give an explicit boundary measurement formula for which does not depend choice extends our recent results Ising model, simultaneously also includes case electrical networks. systematically develop basic properties In particular, study their real totally positive parts, strand diagrams, shift map motivated connection zonotopal tilings scattering amplitudes.