Given a subvariety of the Grassmannian, a standard monomial is a monomial which does not lie in the associated initial ideal. This simple definition has proved a powerful tool for proving certain algebro-geometric properties of the subvariety. In this talk, we'll first consider the standard monomials for the Grassmannian. We'll then look at recent work by Almousa, Gao, and Huang which gives a description of the standard monomials for a positroid variety in terms of a special type of semistandard tableaux.

This talk is based on the delightful paper Standard Monomials for Positroid Varieties by Almousa, Gao, and Huang from 2024.