In 2021, Chepuri, George, and Speyer showed that space of compatified electrical networks constructed by Lam in 2014 coincides with the Lagrangian Grassmannian. The electroid varieties introduced in Lam's original paper thus become a candidate for a stratification for the Lagrangian Grassmannian analogous to the positroid stratification for the Grassmannian. We build on these results and prove that the closed electroid varieties are reduced, irreducible, R1, compatibly F-split, form a stratification for the Lagrangian Grassmannians with expected dimensions, and have expected positive parts. They serve as the algebro-geometric complement to a total positivity story for the Lagrangian Grassmannians.

This talk is based on joint work with David Speyer and Mia Smith. This is a follow-up talk for Mia's talk last week. However, I will not assume that the audience attended Mia's talk from last week.